\(x^2+5x\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(x^2+5x\)?
#factorisation
#common factor
#algebraic identities
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A (x(x+5))
B (x+5)
C (5(x+5))
D (x(x-5))
Explanation opens after your attempt
Correct Answer
A. (x(x+5))
Step 1
Concept
The common factor of \(x^2\) and (5x) is (x). Exam tip: look for the common factor first.
Step 2
Why this answer is correct
The correct answer is A. (x(x+5)). The common factor of \(x^2\) and (5x) is (x). Exam tip: look for the common factor first.
Step 3
Exam Tip
\(x^2\) और (5x) में सामान्य गुणनखंड (x) है। परीक्षा में पहले सामान्य गुणनखंड देखें।
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(3a+6) का गुणनखंड रूप कौन सा है?
Which is the factorised form of (3a+6)?
#common factor
#factorisation
#easy algebra
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A (a+6)
B (3(a+2))
C (6(a+3))
D (3(a-2))
Explanation opens after your attempt
Correct Answer
B. (3(a+2))
Step 1
Concept
Both terms have common factor (3). Exam tip: take out the numerical common factor.
Step 2
Why this answer is correct
The correct answer is B. (3(a+2)). Both terms have common factor (3). Exam tip: take out the numerical common factor.
Step 3
Exam Tip
दोनों पदों में सामान्य गुणनखंड (3) है। परीक्षा में संख्या वाले सामान्य गुणनखंड को बाहर निकालें।
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\(y^2-16\) को किस रूप में गुणनखंडित किया जाएगा?
How will \(y^2-16\) be factorised?
#difference of squares
#factorisation
#identity
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A (y(y-16))
B \(y^2-4^2\)
C ((y-4)(y+4))
D ((y-16)(y+1))
Explanation opens after your attempt
Correct Answer
C. ((y-4)(y+4))
Step 1
Concept
Since \(16=4^2\), this is a difference of two squares. Exam tip: identify (a-2 -b-2 =(a-b)(a+b)).
Step 2
Why this answer is correct
The correct answer is C. ((y-4)(y+4)). Since \(16=4^2\), this is a difference of two squares. Exam tip: identify (a-2 -b-2 =(a-b)(a+b)).
Step 3
Exam Tip
\(16=4^2\), इसलिए यह दो वर्गों का अंतर है। परीक्षा में (a-2 -b-2 =(a-b)(a+b)) पहचानें।
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\(p^2+10p+25\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(p^2+10p+25\)?
#perfect square
#factorisation
#binomial square
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A ((p+10)(p+25))
B ((p-5)2 )
C ((p+2)(p+8))
D ((p+5)2 )
Explanation opens after your attempt
Correct Answer
D. ((p+5)2 )
Step 1
Concept
\(25=5^2\) and \(10p=2\times5\times p\). Exam tip: identify perfect square trinomials.
Step 2
Why this answer is correct
The correct answer is D. ((p+5)2 ). \(25=5^2\) and \(10p=2\times5\times p\). Exam tip: identify perfect square trinomials.
Step 3
Exam Tip
\(25=5^2\) और \(10p=2\times5\times p\) है। परीक्षा में पूर्ण वर्ग त्रिपद को पहचानें।
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\(x^2-6x+9\) किसका वर्ग है?
Whose square is \(x^2-6x+9\)?
#minus square
#perfect square
#factorisation
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A ((x-3)2 )
B ((x+3)2 )
C ((x-6)2 )
D ((x+9)2 )
Explanation opens after your attempt
Correct Answer
A. ((x-3)2 )
Step 1
Concept
Since \(9=3^2\) and the middle term is (-6x), the form is ((x-3)2 ). Exam tip: watch the negative sign.
Step 2
Why this answer is correct
The correct answer is A. ((x-3)2 ). Since \(9=3^2\) and the middle term is (-6x), the form is ((x-3)2 ). Exam tip: watch the negative sign.
Step 3
Exam Tip
\(9=3^2\) और बीच का पद (-6x) है, इसलिए रूप ((x-3)2 ) है। परीक्षा में ऋण चिह्न ध्यान से देखें।
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\(2x^2+8x\) में सामान्य गुणनखंड निकालने पर क्या मिलेगा?
What is obtained after taking out the common factor from \(2x^2+8x\)?
#common factor
#monomial factor
#factorisation
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A (2(x+8))
B (2x(x+4))
C (x(2x+8x))
D (8x(x+2))
Explanation opens after your attempt
Correct Answer
B. (2x(x+4))
Step 1
Concept
Both terms have common factor (2x). Exam tip: check the common numerical and variable parts.
Step 2
Why this answer is correct
The correct answer is B. (2x(x+4)). Both terms have common factor (2x). Exam tip: check the common numerical and variable parts.
Step 3
Exam Tip
दोनों पदों में सामान्य गुणनखंड (2x) है। परीक्षा में चर और संख्या दोनों का सामान्य भाग देखें।
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\(a^2+7a+12\) के सही गुणनखंड कौन से हैं?
What are the correct factors of \(a^2+7a+12\)?
#trinomial factorisation
#middle term
#algebra
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A ((a+1)(a+12))
B ((a+2)(a+6))
C ((a+3)(a+4))
D ((a-3)(a-4))
Explanation opens after your attempt
Correct Answer
C. ((a+3)(a+4))
Step 1
Concept
(3+4=7) and \(3\times4=12\). Exam tip: find two numbers whose sum is the middle coefficient.
Step 2
Why this answer is correct
The correct answer is C. ((a+3)(a+4)). (3+4=7) and \(3\times4=12\). Exam tip: find two numbers whose sum is the middle coefficient.
Step 3
Exam Tip
(3+4=7) और \(3\times4=12\) है। परीक्षा में ऐसे दो संख्याएं खोजें जिनका योग बीच का गुणांक हो।
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\(m^2-9\) का गुणनखंड रूप क्या है?
What is the factorised form of \(m^2-9\)?
#difference of squares
#factorisation
#class 9
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A (m(m-9 ))
B ((m-9 )(m+1))
C ((m-3 )2 )
D ((m-3 )(m+3))
Explanation opens after your attempt
Correct Answer
D. ((m-3 )(m+3))
Step 1
Concept
Since \(9=3^2\), \(m^2-9\) is a difference of squares. Exam tip: identify difference of squares quickly.
Step 2
Why this answer is correct
The correct answer is D. ((m-3 )(m+3)). Since \(9=3^2\), \(m^2-9\) is a difference of squares. Exam tip: identify difference of squares quickly.
Step 3
Exam Tip
\(9=3^2\), इसलिए \(m^2-9\) दो वर्गों का अंतर है। परीक्षा में अंतर के वर्गों को तुरंत पहचानें।
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\(4x^2-25\) को गुणनखंडों में लिखिए।
Write \(4x^2-25\) in factors.
#difference of squares
#coefficient
#factorisation
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A ((2x-5)(2x+5))
B ((4x-5)(4x+5))
C ((2x-25)(2x+1))
D ((x-5)(x+5))
Explanation opens after your attempt
Correct Answer
A. ((2x-5)(2x+5))
Step 1
Concept
(4x-2 =(2x)2 ) and \(25=5^2\). Exam tip: take square roots of both squares.
Step 2
Why this answer is correct
The correct answer is A. ((2x-5)(2x+5)). (4x-2 =(2x)2 ) and \(25=5^2\). Exam tip: take square roots of both squares.
Step 3
Exam Tip
(4x-2 =(2x)2 ) और \(25=5^2\) है। परीक्षा में दोनों वर्गों की वर्गमूल निकालें।
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\(x^2+9x+20\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factorised form of \(x^2+9x+20\)?
#trinomial factorisation
#sum product
#quadratic
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A ((x+2)(x+10))
B ((x+4)(x+5))
C ((x-4)(x-5))
D ((x+1)(x+20))
Explanation opens after your attempt
Correct Answer
B. ((x+4)(x+5))
Step 1
Concept
(4+5=9) and \(4\times5=20\). Exam tip: check both sum and product.
Step 2
Why this answer is correct
The correct answer is B. ((x+4)(x+5)). (4+5=9) and \(4\times5=20\). Exam tip: check both sum and product.
Step 3
Exam Tip
(4+5=9) और \(4\times5=20\) है। परीक्षा में योग और गुणनफल दोनों जांचें।
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(5p+15q) में सामान्य गुणनखंड निकालने पर क्या मिलेगा?
What is obtained by taking out the common factor from (5p+15q)?
#common factor
#factorisation
#linear expression
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A (5(p+3q))
B (5(p+15q))
C (p(5+15q))
D (15(p+q))
Explanation opens after your attempt
Correct Answer
A. (5(p+3q))
Step 1
Concept
(5) is common in both terms. Exam tip: verify by multiplying the outside factor back.
Step 2
Why this answer is correct
The correct answer is A. (5(p+3q)). (5) is common in both terms. Exam tip: verify by multiplying the outside factor back.
Step 3
Exam Tip
दोनों पदों में (5) सामान्य है। परीक्षा में बाहर निकाले गुणनखंड से अंदर के पदों को दोबारा गुणा करके जांचें।
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\(6a^2b+9ab^2\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(6a^2b+9ab^2\)?
#common monomial
#factorisation
#algebra
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A (3a\(2ab+3b^2\))
B (3ab(2a+3b))
C (ab(6a+9b))
D (9ab(2a+3b))
Explanation opens after your attempt
Correct Answer
B. (3ab(2a+3b))
Step 1
Concept
The common factor is (3ab). Exam tip: it is better to take out the greatest common factor.
Step 2
Why this answer is correct
The correct answer is B. (3ab(2a+3b)). The common factor is (3ab). Exam tip: it is better to take out the greatest common factor.
Step 3
Exam Tip
सामान्य गुणनखंड (3ab) है। परीक्षा में सबसे बड़ा सामान्य गुणनखंड निकालना बेहतर होता है।
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\(x^2-49\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2-49\).
#difference of squares
#square number
#factorisation
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A ((x-49)(x+1))
B ((x-7)2 )
C ((x-7)(x+7))
D ((x+7)2 )
Explanation opens after your attempt
Correct Answer
C. ((x-7)(x+7))
Step 1
Concept
Since \(49=7^2\), (x-2 -49=(x-7)(x+7)). Exam tip: identify square numbers.
Step 2
Why this answer is correct
The correct answer is C. ((x-7)(x+7)). Since \(49=7^2\), (x-2 -49=(x-7)(x+7)). Exam tip: identify square numbers.
Step 3
Exam Tip
\(49=7^2\), इसलिए (x-2 -49=(x-7)(x+7)) है। परीक्षा में वर्ग संख्या पहचानें।
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\(y^2+8y+16\) का सही गुणनखंड रूप क्या होगा?
What will be the correct factorised form of \(y^2+8y+16\)?
#perfect square
#binomial factorisation
#identity
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A ((y+8)2 )
B ((y-4)2 )
C ((y+2)(y+8))
D ((y+4)2 )
Explanation opens after your attempt
Correct Answer
D. ((y+4)2 )
Step 1
Concept
\(16=4^2\) and \(8y=2\times4\times y\), so it is ((y+4)2 ). Exam tip: identify the perfect square.
Step 2
Why this answer is correct
The correct answer is D. ((y+4)2 ). \(16=4^2\) and \(8y=2\times4\times y\), so it is ((y+4)2 ). Exam tip: identify the perfect square.
Step 3
Exam Tip
\(16=4^2\) और \(8y=2\times4\times y\), इसलिए यह ((y+4)2 ) है। परीक्षा में पूर्ण वर्ग पहचानें।
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\(a^2-2ab+b^2\) को गुणनखंडित करने पर क्या मिलेगा?
What is obtained by factorising \(a^2-2ab+b^2\)?
#perfect square
#minus identity
#factorisation
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A ((a-b)2 )
B ((a+b)2 )
C ((a-b)(a+b))
D (a(a-2b))
Explanation opens after your attempt
Correct Answer
A. ((a-b)2 )
Step 1
Concept
This is the perfect square identity ((a-b)2 ). Exam tip: use the middle term (-2ab) as a clue.
Step 2
Why this answer is correct
The correct answer is A. ((a-b)2 ). This is the perfect square identity ((a-b)2 ). Exam tip: use the middle term (-2ab) as a clue.
Step 3
Exam Tip
यह ((a-b)2 ) की पूर्ण वर्ग पहचान है। परीक्षा में बीच के पद (-2ab) को संकेत मानें।
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\(10x^2-15x\) का गुणनखंड रूप कौन सा है?
Which is the factorised form of \(10x^2-15x\)?
#common factor
#negative term
#factorisation
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A (10x(x-15))
B (5x(2x-3))
C (5\(2x^2-15x\))
D (15x(10x-1))
Explanation opens after your attempt
Correct Answer
B. (5x(2x-3))
Step 1
Concept
(5x) is common in both terms. Exam tip: keep the negative sign correctly inside.
Step 2
Why this answer is correct
The correct answer is B. (5x(2x-3)). (5x) is common in both terms. Exam tip: keep the negative sign correctly inside.
Step 3
Exam Tip
दोनों पदों में (5x) सामान्य है। परीक्षा में ऋण चिह्न को अंदर सही रखें।
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\(9m^2-1\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(9m^2-1\)?
#difference of squares
#coefficient
#identity
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A ((9m-1)(9m+1))
B ((3m-1)2 )
C (m(9m-1))
D ((3m-1)(3m+1))
Explanation opens after your attempt
Correct Answer
D. ((3m-1)(3m+1))
Step 1
Concept
(9m-2 =(3m)2 ) and \(1=1^2\). Exam tip: apply the difference of squares formula.
Step 2
Why this answer is correct
The correct answer is D. ((3m-1)(3m+1)). (9m-2 =(3m)2 ) and \(1=1^2\). Exam tip: apply the difference of squares formula.
Step 3
Exam Tip
(9m-2 =(3m)2 ) और \(1=1^2\) है। परीक्षा में अंतर के वर्गों का सूत्र लगाएं।
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\(4a^2+12a+9\) किस रूप में लिखा जाएगा?
In which form will \(4a^2+12a+9\) be written?
#perfect square
#coefficient square
#factorisation
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A ((2a+3)2 )
B ((4a+3)2 )
C ((2a-3)2 )
D ((a+3)(a+4))
Explanation opens after your attempt
Correct Answer
A. ((2a+3)2 )
Step 1
Concept
(4a-2 =(2a)2 ), \(9=3^2\), and \(12a=2\times2a\times3\). Exam tip: match all three terms.
Step 2
Why this answer is correct
The correct answer is A. ((2a+3)2 ). (4a-2 =(2a)2 ), \(9=3^2\), and \(12a=2\times2a\times3\). Exam tip: match all three terms.
Step 3
Exam Tip
(4a-2 =(2a)2 ), \(9=3^2\) और \(12a=2\times2a\times3\) है। परीक्षा में तीनों पद मिलाएं।
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(7xy+14x) का सही गुणनखंड रूप चुनिए।
Choose the correct factorised form of (7xy+14x).
#common factor
#two terms
#factorisation
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A (7(y+14x))
B (7x(y+2))
C (xy(7+14))
D (14x(y+7))
Explanation opens after your attempt
Correct Answer
B. (7x(y+2))
Step 1
Concept
(7x) is common in both terms. Exam tip: check the outside factor in both terms.
Step 2
Why this answer is correct
The correct answer is B. (7x(y+2)). (7x) is common in both terms. Exam tip: check the outside factor in both terms.
Step 3
Exam Tip
दोनों पदों में (7x) सामान्य है। परीक्षा में बाहर निकले गुणनखंड को दोनों पदों में जांचें।
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\(x^2+3x+2\) को गुणनखंडित कीजिए।
Factorise \(x^2+3x+2\).
#trinomial
#easy factorisation
#middle term
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A ((x+1)(x+2))
B ((x+3)(x+2))
C ((x-1)(x-2))
D ((x+1)(x+3))
Explanation opens after your attempt
Correct Answer
A. ((x+1)(x+2))
Step 1
Concept
(1+2=3) and \(1\times2=2\), so these are correct factors. Exam tip: start with small numbers.
Step 2
Why this answer is correct
The correct answer is A. ((x+1)(x+2)). (1+2=3) and \(1\times2=2\), so these are correct factors. Exam tip: start with small numbers.
Step 3
Exam Tip
(1+2=3) और \(1\times2=2\), इसलिए ये सही गुणनखंड हैं। परीक्षा में छोटी संख्याओं से शुरुआत करें।
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\(12p^2q-8pq^2\) में सामान्य गुणनखंड निकालने पर क्या मिलेगा?
What is obtained by taking out the common factor from \(12p^2q-8pq^2\)?
#monomial factor
#greatest common factor
#factorisation
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A (2pq(6p-4q))
B (4pq(3p-2q))
C (8pq(12p-q))
D (4p\(3pq-2q^2\))
Explanation opens after your attempt
Correct Answer
B. (4pq(3p-2q))
Step 1
Concept
The greatest common factor is (4pq). Exam tip: find common variables and numbers in every term.
Step 2
Why this answer is correct
The correct answer is B. (4pq(3p-2q)). The greatest common factor is (4pq). Exam tip: find common variables and numbers in every term.
Step 3
Exam Tip
सबसे बड़ा सामान्य गुणनखंड (4pq) है। परीक्षा में हर पद में सामान्य चर और संख्या खोजें।
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\(z^2-4z+4\) का गुणनखंड रूप क्या है?
What is the factorised form of \(z^2-4z+4\)?
#minus square
#perfect square
#factorisation
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A ((z+2)2 )
B (z(z-4)+4)
C ((z-2)2 )
D ((z-4)(z+1))
Explanation opens after your attempt
Correct Answer
C. ((z-2)2 )
Step 1
Concept
\(4=2^2\) and \(-4z=-2\times z\times2\), so it is ((z-2)2 ). Exam tip: identify subtraction perfect squares.
Step 2
Why this answer is correct
The correct answer is C. ((z-2)2 ). \(4=2^2\) and \(-4z=-2\times z\times2\), so it is ((z-2)2 ). Exam tip: identify subtraction perfect squares.
Step 3
Exam Tip
\(4=2^2\) और \(-4z=-2\times z\times2\), इसलिए ((z-2)2 ) है। परीक्षा में घटाव वाले पूर्ण वर्ग को पहचानें।
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\(x^2+2xy+y^2\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(x^2+2xy+y^2\)?
#perfect square
#two variables
#factorisation
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? Hint Small clue
A ((x-y)2 )
B ((x+y)(x-y))
C (x(x+2y))
D ((x+y)2 )
Explanation opens after your attempt
Correct Answer
D. ((x+y)2 )
Step 1
Concept
This is a perfect square trinomial in (x) and (y). Exam tip: connect (2xy) with two equal terms.
Step 2
Why this answer is correct
The correct answer is D. ((x+y)2 ). This is a perfect square trinomial in (x) and (y). Exam tip: connect (2xy) with two equal terms.
Step 3
Exam Tip
यह (x) और (y) का पूर्ण वर्ग त्रिपद है। परीक्षा में (2xy) को दो समान पदों से जोड़ें।
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\(a^2+5a+6\) के गुणनखंड कौन से हैं?
What are the factors of \(a^2+5a+6\)?
#trinomial factorisation
#easy quadratic
#algebra
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? Hint Small clue
A ((a+2)(a+3))
B ((a+1)(a+6))
C ((a-2)(a-3))
D ((a+5)(a+6))
Explanation opens after your attempt
Correct Answer
A. ((a+2)(a+3))
Step 1
Concept
(2+3=5) and \(2\times3=6\), so the factors are correct. Exam tip: check factors of the last term.
Step 2
Why this answer is correct
The correct answer is A. ((a+2)(a+3)). (2+3=5) and \(2\times3=6\), so the factors are correct. Exam tip: check factors of the last term.
Step 3
Exam Tip
(2+3=5) और \(2\times3=6\), इसलिए गुणनखंड सही हैं। परीक्षा में अंतिम पद के गुणनखंड देखें।
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\(16n^2-25\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(16n^2-25\)?
#difference of squares
#coefficient
#factorisation
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? Hint Small clue
A ((16n-5)(16n+5))
B ((4n-5)(4n+5))
C ((4n-25)(4n+1))
D ((n-5)(n+5))
Explanation opens after your attempt
Correct Answer
B. ((4n-5)(4n+5))
Step 1
Concept
(16n-2 =(4n)2 ) and \(25=5^2\). Exam tip: take the square root with the coefficient.
Step 2
Why this answer is correct
The correct answer is B. ((4n-5)(4n+5)). (16n-2 =(4n)2 ) and \(25=5^2\). Exam tip: take the square root with the coefficient.
Step 3
Exam Tip
(16n-2 =(4n)2 ) और \(25=5^2\) है। परीक्षा में गुणांक सहित वर्गमूल निकालें।
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(8x+12) का सबसे सरल गुणनखंड रूप कौन सा है?
Which is the simplest factorised form of (8x+12)?
#greatest common factor
#simple factorisation
#linear
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A (2(4x+6))
B (8(x+12))
C (4(2x+3))
D (12(8x+1))
Explanation opens after your attempt
Correct Answer
C. (4(2x+3))
Step 1
Concept
The greatest common factor of (8x) and (12) is (4). Exam tip: take the greatest factor for the simplest form.
Step 2
Why this answer is correct
The correct answer is C. (4(2x+3)). The greatest common factor of (8x) and (12) is (4). Exam tip: take the greatest factor for the simplest form.
Step 3
Exam Tip
(8x) और (12) का सबसे बड़ा सामान्य गुणनखंड (4) है। परीक्षा में सरलतम रूप के लिए सबसे बड़ा गुणनखंड निकालें।
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\(9x^2+6x+1\) किसका वर्ग है?
Whose square is \(9x^2+6x+1\)?
#perfect square
#coefficient
#binomial
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? Hint Small clue
A ((9x+1)2 )
B ((3x-1)2 )
C ((x+3)2 )
D ((3x+1)2 )
Explanation opens after your attempt
Correct Answer
D. ((3x+1)2 )
Step 1
Concept
(9x-2 =(3x)2 ), \(1=1^2\), and \(6x=2\times3x\times1\). Exam tip: match the perfect square pattern.
Step 2
Why this answer is correct
The correct answer is D. ((3x+1)2 ). (9x-2 =(3x)2 ), \(1=1^2\), and \(6x=2\times3x\times1\). Exam tip: match the perfect square pattern.
Step 3
Exam Tip
(9x-2 =(3x)2 ), \(1=1^2\) और \(6x=2\times3x\times1\) है। परीक्षा में पूर्ण वर्ग पैटर्न मिलाएं।
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\(b^2-b-20\) के गुणनखंड कौन से हैं?
What are the factors of \(b^2-b-20\)?
#signed factorisation
#trinomial
#quadratic
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? Hint Small clue
A ((b-5)(b+4))
B ((b+5)(b+4))
C ((b-4)(b+5))
D ((b-20)(b+1))
Explanation opens after your attempt
Correct Answer
A. ((b-5)(b+4))
Step 1
Concept
(-5+4=-1) and \(-5\times4=-20\). Exam tip: choose opposite signs for a negative product.
Step 2
Why this answer is correct
The correct answer is A. ((b-5)(b+4)). (-5+4=-1) and \(-5\times4=-20\). Exam tip: choose opposite signs for a negative product.
Step 3
Exam Tip
(-5+4=-1) और \(-5\times4=-20\) है। परीक्षा में ऋणात्मक गुणनफल के लिए विपरीत चिन्ह चुनें।
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\(x^2-10x+25\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2-10x+25\).
#minus perfect square
#factorisation
#identity
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? Hint Small clue
A ((x+5)2 )
B ((x-5)2 )
C ((x-10)(x+25))
D ((x-25)2 )
Explanation opens after your attempt
Correct Answer
B. ((x-5)2 )
Step 1
Concept
\(25=5^2\) and \(-10x=-2\times5\times x\). Exam tip: identify the negative perfect square.
Step 2
Why this answer is correct
The correct answer is B. ((x-5)2 ). \(25=5^2\) and \(-10x=-2\times5\times x\). Exam tip: identify the negative perfect square.
Step 3
Exam Tip
\(25=5^2\) और \(-10x=-2\times5\times x\) है। परीक्षा में ऋणात्मक पूर्ण वर्ग पहचानें।
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\(14a^2+21a\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(14a^2+21a\)?
#common factor
#monomial factor
#factorisation
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A (7\(2a^2+3a\))
B (14a(a+21))
C (7a(2a+3))
D (21a(14a+1))
Explanation opens after your attempt
Correct Answer
C. (7a(2a+3))
Step 1
Concept
(7a) is common in both terms. Exam tip: divide the terms by (7a) to write the inside.
Step 2
Why this answer is correct
The correct answer is C. (7a(2a+3)). (7a) is common in both terms. Exam tip: divide the terms by (7a) to write the inside.
Step 3
Exam Tip
दोनों पदों में (7a) सामान्य है। परीक्षा में पदों को (7a) से भाग देकर अंदर लिखें।
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\(r^2+13r+36\) के सही गुणनखंड कौन से हैं?
What are the correct factors of \(r^2+13r+36\)?
#trinomial
#factor pair
#factorisation
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A ((r+3)(r+12))
B ((r+4)(r+9))
C ((r-4)(r-9))
D ((r+6)(r+6))
Explanation opens after your attempt
Correct Answer
B. ((r+4)(r+9))
Step 1
Concept
(4+9=13) and \(4\times9=36\). Exam tip: choose the correct pair from factors of the last term.
Step 2
Why this answer is correct
The correct answer is B. ((r+4)(r+9)). (4+9=13) and \(4\times9=36\). Exam tip: choose the correct pair from factors of the last term.
Step 3
Exam Tip
(4+9=13) और \(4\times9=36\) है। परीक्षा में अंतिम पद के कारकों से सही जोड़ी चुनें।
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\(25x^2-y^2\) को गुणनखंडित कीजिए।
Factorise \(25x^2-y^2\).
#difference of squares
#two variables
#factorisation
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? Hint Small clue
A ((25x-y)(25x+y))
B ((5x-y)2 )
C ((5x-y)(5x+y))
D ((x-y)(x+y))
Explanation opens after your attempt
Correct Answer
C. ((5x-y)(5x+y))
Step 1
Concept
(25x-2 =(5x)2 ) and \(y^2\) is the second square. Exam tip: use the form ((A-B)(A+B)).
Step 2
Why this answer is correct
The correct answer is C. ((5x-y)(5x+y)). (25x-2 =(5x)2 ) and \(y^2\) is the second square. Exam tip: use the form ((A-B)(A+B)).
Step 3
Exam Tip
(25x-2 =(5x)2 ) और \(y^2\) दूसरा वर्ग है। परीक्षा में ((A-B)(A+B)) का रूप लगाएं।
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\(m^2+2mn+n^2\) का गुणनखंड रूप कौन सा है?
Which is the factorised form of \(m^2+2mn+n^2\)?
#perfect square
#two variables
#identity
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? Hint Small clue
A ((m-n)2 )
B (m(m+2n))
C ((m+n)(m-n))
D ((m+n)2 )
Explanation opens after your attempt
Correct Answer
D. ((m+n)2 )
Step 1
Concept
This is a perfect square trinomial in (m) and (n). Exam tip: understand (2mn) as two equal terms.
Step 2
Why this answer is correct
The correct answer is D. ((m+n)2 ). This is a perfect square trinomial in (m) and (n). Exam tip: understand (2mn) as two equal terms.
Step 3
Exam Tip
यह (m) और (n) का पूर्ण वर्ग त्रिपद है। परीक्षा में (2mn) को दो समान पदों से समझें।
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\(c^2-6c+8\) के गुणनखंड क्या हैं?
What are the factors of \(c^2-6c+8\)?
#signed trinomial
#factorisation
#quadratic
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? Hint Small clue
A ((c-2)(c-4))
B ((c+2)(c+4))
C ((c-1)(c-8))
D ((c+2)(c-4))
Explanation opens after your attempt
Correct Answer
A. ((c-2)(c-4))
Step 1
Concept
(-2-4=-6) and \((-2)\times(-4)=8\). Exam tip: for positive last term and negative middle term, take both signs negative.
Step 2
Why this answer is correct
The correct answer is A. ((c-2)(c-4)). (-2-4=-6) and \((-2)\times(-4)=8\). Exam tip: for positive last term and negative middle term, take both signs negative.
Step 3
Exam Tip
(-2-4=-6) और \((-2)\times(-4)=8\) है। परीक्षा में धनात्मक अंतिम पद और ऋणात्मक मध्य पद के लिए दोनों चिह्न ऋणात्मक लें।
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(18xy-24y) का सबसे बड़ा सामान्य गुणनखंड निकालने पर क्या मिलेगा?
What is obtained by taking out the greatest common factor from (18xy-24y)?
#greatest common factor
#two terms
#factorisation
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? Hint Small clue
A (3y(6x-8))
B (6y(3x-4))
C (18y(x-24))
D (24y(18x-1))
Explanation opens after your attempt
Correct Answer
B. (6y(3x-4))
Step 1
Concept
The greatest common factor of (18xy) and (24y) is (6y). Exam tip: check numbers and variables together.
Step 2
Why this answer is correct
The correct answer is B. (6y(3x-4)). The greatest common factor of (18xy) and (24y) is (6y). Exam tip: check numbers and variables together.
Step 3
Exam Tip
(18xy) और (24y) में सबसे बड़ा सामान्य गुणनखंड (6y) है। परीक्षा में संख्या और चर दोनों को साथ देखें।
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\(x^2-1\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2-1\).
#difference of squares
#basic factorisation
#identity
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? Hint Small clue
A (x(x-1))
B ((x-1)2 )
C ((x-1)(x+1))
D ((x+1)2 )
Explanation opens after your attempt
Correct Answer
C. ((x-1)(x+1))
Step 1
Concept
Since \(1=1^2\), \(x^2-1\) is a difference of squares. Exam tip: apply small identities carefully.
Step 2
Why this answer is correct
The correct answer is C. ((x-1)(x+1)). Since \(1=1^2\), \(x^2-1\) is a difference of squares. Exam tip: apply small identities carefully.
Step 3
Exam Tip
\(1=1^2\), इसलिए \(x^2-1\) दो वर्गों का अंतर है। परीक्षा में छोटी पहचान भी ध्यान से लगाएं।
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\(2a^2+5a+2\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(2a^2+5a+2\)?
#splitting middle term
#factorisation
#quadratic
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? Hint Small clue
A ((2a+2)(a+1))
B ((2a+1)(a+2))
C ((a+1)(a+2))
D ((2a-1)(a-2))
Explanation opens after your attempt
Correct Answer
B. ((2a+1)(a+2))
Step 1
Concept
Expanding ((2a+1)(a+2)) gives \(2a^2+5a+2\). Exam tip: verify the answer by multiplication.
Step 2
Why this answer is correct
The correct answer is B. ((2a+1)(a+2)). Expanding ((2a+1)(a+2)) gives \(2a^2+5a+2\). Exam tip: verify the answer by multiplication.
Step 3
Exam Tip
((2a+1)(a+2)) फैलाने पर \(2a^2+5a+2\) मिलता है। परीक्षा में गुणा करके उत्तर की जांच करें।
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\(q^2+6q+5\) के गुणनखंड कौन से हैं?
What are the factors of \(q^2+6q+5\)?
#trinomial
#sum product
#factorisation
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? Hint Small clue
A ((q+2)(q+3))
B ((q-1)(q-5))
C ((q+1)(q+5))
D ((q+6)(q+5))
Explanation opens after your attempt
Correct Answer
C. ((q+1)(q+5))
Step 1
Concept
(1+5=6) and \(1\times5=5\), so the correct pair is (1) and (5). Exam tip: match sum and product.
Step 2
Why this answer is correct
The correct answer is C. ((q+1)(q+5)). (1+5=6) and \(1\times5=5\), so the correct pair is (1) and (5). Exam tip: match sum and product.
Step 3
Exam Tip
(1+5=6) और \(1\times5=5\), इसलिए सही जोड़ी (1) और (5) है। परीक्षा में योग और गुणनफल मिलाएं।
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\(36p^2-49q^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(36p^2-49q^2\)?
#difference of squares
#two variables
#factorisation
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? Hint Small clue
A ((36p-49q)(36p+49q))
B ((6p-7q)2 )
C ((6p-q)(6p+49q))
D ((6p-7q)(6p+7q))
Explanation opens after your attempt
Correct Answer
D. ((6p-7q)(6p+7q))
Step 1
Concept
(36p-2 =(6p)2 ) and (49q-2 =(7q)2 ). Exam tip: form factors from square roots of both squares.
Step 2
Why this answer is correct
The correct answer is D. ((6p-7q)(6p+7q)). (36p-2 =(6p)2 ) and (49q-2 =(7q)2 ). Exam tip: form factors from square roots of both squares.
Step 3
Exam Tip
(36p-2 =(6p)2 ) और (49q-2 =(7q)2 ) है। परीक्षा में दोनों वर्गों की वर्गमूल से गुणनखंड बनाएं।
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\(15x^2y+20xy^2\) का सही गुणनखंड रूप कौन सा है?
Which is the correct factorised form of \(15x^2y+20xy^2\)?
#common factor
#two variables
#factorisation
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? Hint Small clue
A (5xy(3x+4y))
B (5x\(3xy+4y^2\))
C (15xy(x+20y))
D (20xy(15x+1))
Explanation opens after your attempt
Correct Answer
A. (5xy(3x+4y))
Step 1
Concept
The greatest common factor in both terms is (5xy). Exam tip: keep the inside terms simplified.
Step 2
Why this answer is correct
The correct answer is A. (5xy(3x+4y)). The greatest common factor in both terms is (5xy). Exam tip: keep the inside terms simplified.
Step 3
Exam Tip
दोनों पदों में सबसे बड़ा सामान्य गुणनखंड (5xy) है। परीक्षा में अंदर के पदों को सरल रखें।
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\(s^2-12s+36\) का गुणनखंड रूप क्या है?
What is the factorised form of \(s^2-12s+36\)?
#minus perfect square
#factorisation
#identity
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? Hint Small clue
A ((s+6)2 )
B ((s-6 )2 )
C ((s-12 )(s+3))
D ((s-3 )(s-12 ))
Explanation opens after your attempt
Correct Answer
B. ((s-6 )2 )
Step 1
Concept
\(36=6^2\) and \(-12s=-2\times6\times s\). Exam tip: check the middle term in a perfect square.
Step 2
Why this answer is correct
The correct answer is B. ((s-6 )2 ). \(36=6^2\) and \(-12s=-2\times6\times s\). Exam tip: check the middle term in a perfect square.
Step 3
Exam Tip
\(36=6^2\) और \(-12s=-2\times6\times s\) है। परीक्षा में पूर्ण वर्ग में मध्य पद की जांच करें।
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\(x^2+15x+56\) को गुणनखंडित करने के लिए कौन सी जोड़ी सही है?
Which pair is correct for factorising \(x^2+15x+56\)?
#factor pair
#trinomial
#factorisation
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A (6) और (9) / (6) and (9)
B (4) और (14) / (4) and (14)
C (7) और (8) / (7) and (8)
D (5) और (10) / (5) and (10)
Explanation opens after your attempt
Correct Answer
C. (7) और (8) / (7) and (8)
Step 1
Concept
(7+8=15) and \(7\times8=56\). Exam tip: after finding the pair, write ((x+7)(x+8)).
Step 2
Why this answer is correct
The correct answer is C. (7) और (8) / (7) and (8). (7+8=15) and \(7\times8=56\). Exam tip: after finding the pair, write ((x+7)(x+8)).
Step 3
Exam Tip
(7+8=15) और \(7\times8=56\) है। परीक्षा में सही जोड़ी मिलने पर गुणनखंड ((x+7)(x+8)) लिखें।
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\(27a^3-9a^2\) में सामान्य गुणनखंड निकालने पर क्या मिलेगा?
What is obtained by taking out the common factor from \(27a^3-9a^2\)?
#common factor
#powers
#factorisation
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A (9a\(3a^2-a\))
B (27a-2 (a-9))
C (a-2 (27a-9))
D (9a-2 (3a-1))
Explanation opens after your attempt
Correct Answer
D. (9a-2 (3a-1))
Step 1
Concept
\(9a^2\) is common in both terms. Exam tip: take out the common variable with the smaller power.
Step 2
Why this answer is correct
The correct answer is D. (9a-2 (3a-1)). \(9a^2\) is common in both terms. Exam tip: take out the common variable with the smaller power.
Step 3
Exam Tip
दोनों पदों में \(9a^2\) सामान्य है। परीक्षा में सबसे कम घात वाला समान चर बाहर निकालें।
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\(49u^2+14uv+v^2\) किसका पूर्ण वर्ग है?
Whose perfect square is \(49u^2+14uv+v^2\)?
#perfect square
#two variables
#factorisation
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A ((7u+v)2 )
B ((49u+v)2 )
C ((7u-v)2 )
D ((u+7v)2 )
Explanation opens after your attempt
Correct Answer
A. ((7u+v)2 )
Step 1
Concept
(49u-2 =(7u)2 ), \(v^2\), and \(14uv=2\times7u\times v\). Exam tip: take square roots of both square terms.
Step 2
Why this answer is correct
The correct answer is A. ((7u+v)2 ). (49u-2 =(7u)2 ), \(v^2\), and \(14uv=2\times7u\times v\). Exam tip: take square roots of both square terms.
Step 3
Exam Tip
(49u-2 =(7u)2 ), \(v^2\) और \(14uv=2\times7u\times v\) है। परीक्षा में दोनों वर्ग पदों की वर्गमूल लें।
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\(y^2-11y+24\) के सही गुणनखंड कौन से हैं?
What are the correct factors of \(y^2-11y+24\)?
#signed trinomial
#factorisation
#quadratic
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A ((y+3)(y+8))
B ((y-3)(y-8))
C ((y-4)(y-6))
D ((y+2)(y+12))
Explanation opens after your attempt
Correct Answer
B. ((y-3)(y-8))
Step 1
Concept
(-3-8=-11) and \((-3)\times(-8)=24\). Exam tip: two negative signs give a positive last term.
Step 2
Why this answer is correct
The correct answer is B. ((y-3)(y-8)). (-3-8=-11) and \((-3)\times(-8)=24\). Exam tip: two negative signs give a positive last term.
Step 3
Exam Tip
(-3-8=-11) और \((-3)\times(-8)=24\) है। परीक्षा में दोनों ऋणात्मक चिह्नों से धनात्मक अंतिम पद मिलता है।
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\(32m^2n-40mn^2\) का सरल गुणनखंड रूप क्या है?
What is the simple factorised form of \(32m^2n-40mn^2\)?
#greatest common factor
#two variables
#factorisation
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A (4mn(8m-10n))
B (8mn(4m-5n))
C (32mn(m-40n))
D (40mn(32m-n))
Explanation opens after your attempt
Correct Answer
B. (8mn(4m-5n))
Step 1
Concept
The greatest common factor is (8mn). Exam tip: keep the answer in the simplest form.
Step 2
Why this answer is correct
The correct answer is B. (8mn(4m-5n)). The greatest common factor is (8mn). Exam tip: keep the answer in the simplest form.
Step 3
Exam Tip
सबसे बड़ा सामान्य गुणनखंड (8mn) है। परीक्षा में उत्तर को सबसे सरल रूप में रखें।
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\(x^2+4xy+4y^2\) को किस रूप में लिखा जाएगा?
In which form will \(x^2+4xy+4y^2\) be written?
#perfect square
#two variables
#identity
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A ((x+4y)2 )
B ((x-2y)2 )
C ((x+2y)2 )
D ((x+2y)(x-2y))
Explanation opens after your attempt
Correct Answer
C. ((x+2y)2 )
Step 1
Concept
(4y-2 =(2y)2 ) and \(4xy=2\times x\times2y\). Exam tip: take the square root of the second square term correctly.
Step 2
Why this answer is correct
The correct answer is C. ((x+2y)2 ). (4y-2 =(2y)2 ) and \(4xy=2\times x\times2y\). Exam tip: take the square root of the second square term correctly.
Step 3
Exam Tip
(4y-2 =(2y)2 ) और \(4xy=2\times x\times2y\) है। परीक्षा में दूसरे वर्ग पद की वर्गमूल सही लें।
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\(81-a^2\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(81-a^2\)?
#difference of squares
#reverse order
#factorisation
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A ((81-a)(81+a))
B ((9-a)2 )
C ((a-9)(a+9))
D ((9-a)(9+a))
Explanation opens after your attempt
Correct Answer
D. ((9-a)(9+a))
Step 1
Concept
Since \(81=9^2\), (81-a-2 =(9-a)(9+a)). Exam tip: take (9) as the square root of the first term.
Step 2
Why this answer is correct
The correct answer is D. ((9-a)(9+a)). Since \(81=9^2\), (81-a-2 =(9-a)(9+a)). Exam tip: take (9) as the square root of the first term.
Step 3
Exam Tip
\(81=9^2\), इसलिए (81-a-2 =(9-a)(9+a)) है। परीक्षा में पहले पद की वर्गमूल (9) लें।
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\(t^2+t-6\) के गुणनखंड कौन से हैं?
What are the factors of \(t^2+t-6\)?
#signed trinomial
#factorisation
#middle term
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A ((t+3)(t-2))
B ((t-3)(t+2))
C ((t+1)(t-6))
D ((t+6)(t-1))
Explanation opens after your attempt
Correct Answer
A. ((t+3)(t-2))
Step 1
Concept
(3+(-2)=1) and \(3\times(-2)=-6\). Exam tip: use opposite signs for a negative last term.
Step 2
Why this answer is correct
The correct answer is A. ((t+3)(t-2)). (3+(-2)=1) and \(3\times(-2)=-6\). Exam tip: use opposite signs for a negative last term.
Step 3
Exam Tip
(3+(-2)=1) और \(3\times(-2)=-6\) है। परीक्षा में ऋणात्मक अंतिम पद के लिए विपरीत चिन्ह लें।
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\(x^2-14x+49\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(x^2-14x+49\)?
#perfect square
#minus square
#factorisation
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A ((x+7)2 )
B ((x-7)2 )
C ((x-14)(x+49))
D ((x-49)2 )
Explanation opens after your attempt
Correct Answer
B. ((x-7)2 )
Step 1
Concept
\(49=7^2\) and \(-14x=-2\times7\times x\). Exam tip: identify ((a-b)2 ) from the negative middle term.
Step 2
Why this answer is correct
The correct answer is B. ((x-7)2 ). \(49=7^2\) and \(-14x=-2\times7\times x\). Exam tip: identify ((a-b)2 ) from the negative middle term.
Step 3
Exam Tip
\(49=7^2\) और \(-14x=-2\times7\times x\) है। परीक्षा में ऋणात्मक मध्य पद देखकर ((a-b)2 ) पहचानें।
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