(6x+9) का गुणनखंडन करते समय सबसे बड़ा समान गुणनखंड कौन सा है?
What is the greatest common factor while factorising (6x+9)?
#factorisation
#common factor
#gcf
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A (3)
B (6)
C (9)
D (x)
Explanation opens after your attempt
Step 1
Concept
(3) is common in both (6x) and (9). Exam tip: first look for the numerical common factor.
Step 2
Why this answer is correct
The correct answer is A. (3). (3) is common in both (6x) and (9). Exam tip: first look for the numerical common factor.
Step 3
Exam Tip
(6x) और (9) दोनों में (3) समान है। परीक्षा में पहले संख्यात्मक समान गुणनखंड देखें।
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(4a+8) का सही गुणनखंडन कौन सा है?
Which is the correct factorisation of (4a+8)?
#common factor
#factorisation
#linear expression
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A (4(a+8))
B (4(a+2))
C (8(a+4))
D (a(4+8))
Explanation opens after your attempt
Correct Answer
B. (4(a+2))
Step 1
Concept
(4) is common in both terms and (4a+8=4(a+2)). Exam tip: multiply back the factor taken out to check.
Step 2
Why this answer is correct
The correct answer is B. (4(a+2)). (4) is common in both terms and (4a+8=4(a+2)). Exam tip: multiply back the factor taken out to check.
Step 3
Exam Tip
दोनों पदों में (4) समान है और (4a+8=4(a+2)) है। परीक्षा में बाहर निकाले गए गुणनखंड को दोबारा गुणा करके जांचें।
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(xy+xz) में कौन सा समान गुणनखंड निकलेगा?
Which common factor will be taken out from (xy+xz)?
#common variable
#factorisation
#algebra
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A (y)
B (z)
C (x)
D (yz)
Explanation opens after your attempt
Step 1
Concept
(x) is common in both terms. Therefore (xy+xz=x(y+z)).
Step 2
Why this answer is correct
The correct answer is C. (x). (x) is common in both terms. Therefore (xy+xz=x(y+z)).
Step 3
Exam Tip
दोनों पदों में (x) समान है। इसलिए (xy+xz=x(y+z)) होगा।
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(5m-15) का सही गुणनखंडन चुनिए।
Choose the correct factorisation of (5m-15).
#common factor
#negative sign
#factorisation
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A (5(m+3))
B (15(m-5 ))
C (m(5-15))
D (5(m-3 ))
Explanation opens after your attempt
Correct Answer
D. (5(m-3 ))
Step 1
Concept
(5) is common in both terms and \(15\div5=3\). Exam tip: keep the negative sign correctly inside the bracket.
Step 2
Why this answer is correct
The correct answer is D. (5(m-3 )). (5) is common in both terms and \(15\div5=3\). Exam tip: keep the negative sign correctly inside the bracket.
Step 3
Exam Tip
दोनों पदों में (5) समान है और \(15\div5=3\) है। परीक्षा में ऋण चिह्न को कोष्ठक के अंदर सही रखें।
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\(a^2+ab\) का गुणनखंडन क्या होगा?
What is the factorisation of \(a^2+ab\)?
#common factor
#variable factor
#algebraic expression
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A (a(a+b))
B (a(a-b))
C (b(a+b))
D (ab(a+1))
Explanation opens after your attempt
Correct Answer
A. (a(a+b))
Step 1
Concept
(a) is common in both terms. So (a-2 +ab=a(a+b)).
Step 2
Why this answer is correct
The correct answer is A. (a(a+b)). (a) is common in both terms. So (a-2 +ab=a(a+b)).
Step 3
Exam Tip
दोनों पदों में (a) समान है। इसलिए (a-2 +ab=a(a+b)) है।
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\(12x^2+18x\) में सबसे बड़ा समान गुणनखंड कौन सा है?
What is the greatest common factor in \(12x^2+18x\)?
#greatest common factor
#monomial factor
#factorisation
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A (6)
B (6x)
C (12x)
D (18x)
Explanation opens after your attempt
Step 1
Concept
(6) is common in the numbers and (x) is common in both terms. So the common factor is (6x).
Step 2
Why this answer is correct
The correct answer is B. (6x). (6) is common in the numbers and (x) is common in both terms. So the common factor is (6x).
Step 3
Exam Tip
संख्याओं में (6) और दोनों पदों में (x) समान है। इसलिए समान गुणनखंड (6x) है।
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\(x^2-9\) का गुणनखंडन किस पहचान से होगा?
Which identity is used to factorise \(x^2-9\)?
#difference of squares
#identity
#factorisation
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A ((a+b)2 )
B ((a-b)2 )
C (a-2 -b-2 =(a-b)(a+b))
D (a(b+c)=ab+ac)
Explanation opens after your attempt
Correct Answer
C. (a-2 -b-2 =(a-b)(a+b))
Step 1
Concept
\(x^2-9=x^2-3^2\), so the difference of squares identity is used. Exam tip: identify both terms as squares.
Step 2
Why this answer is correct
The correct answer is C. (a-2 -b-2 =(a-b)(a+b)). \(x^2-9=x^2-3^2\), so the difference of squares identity is used. Exam tip: identify both terms as squares.
Step 3
Exam Tip
\(x^2-9=x^2-3^2\) है इसलिए वर्गों के अंतर की पहचान लगेगी। परीक्षा में दोनों पदों को वर्ग के रूप में पहचानें।
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\(x^2-16\) का सही गुणनखंडन कौन सा है?
Which is the correct factorisation of \(x^2-16\)?
#difference of squares
#factors
#algebraic identity
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A ((x-16)(x+16))
B ((x-4)2 )
C ((x+4)2 )
D ((x-4)(x+4))
Explanation opens after your attempt
Correct Answer
D. ((x-4)(x+4))
Step 1
Concept
\(16=4^2\), so (x-2 -16=(x-4)(x+4)). Exam tip: in difference of squares, write both sum and difference factors.
Step 2
Why this answer is correct
The correct answer is D. ((x-4)(x+4)). \(16=4^2\), so (x-2 -16=(x-4)(x+4)). Exam tip: in difference of squares, write both sum and difference factors.
Step 3
Exam Tip
\(16=4^2\) है इसलिए (x-2 -16=(x-4)(x+4)) होगा। परीक्षा में वर्गों के अंतर में योग और अंतर दोनों कारक लिखें।
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\(a^2+2ab+b^2\) का गुणनखंडन क्या है?
What is the factorisation of \(a^2+2ab+b^2\)?
#perfect square trinomial
#factorisation
#identity
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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 a perfect square trinomial because the middle term is (2ab). Exam tip: check the roots of the first and last terms.
Step 2
Why this answer is correct
The correct answer is A. ((a+b)2 ). This is a perfect square trinomial because the middle term is (2ab). Exam tip: check the roots of the first and last terms.
Step 3
Exam Tip
यह पूर्ण वर्ग त्रिपद है क्योंकि बीच का पद (2ab) है। परीक्षा में पहले और अंतिम पदों की जड़ें देखें।
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\(x^2+6x+9\) किसका वर्ग है?
\(x^2+6x+9\) is the square of what?
#perfect square
#binomial square
#factorisation
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A (x+6)
B (x+3)
C (x-3)
D (x+9)
Explanation opens after your attempt
Step 1
Concept
\(9=3^2\) and \(6x=2\cdot3x\). Therefore it is ((x+3)2 ).
Step 2
Why this answer is correct
The correct answer is B. (x+3). \(9=3^2\) and \(6x=2\cdot3x\). Therefore it is ((x+3)2 ).
Step 3
Exam Tip
\(9=3^2\) और \(6x=2\cdot3x\) है। इसलिए यह ((x+3)2 ) है।
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\(y^2-10y+25\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(y^2-10y+25\)?
#minus square
#perfect square
#factorisation
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A ((y+5)2 )
B ((y-10)2 )
C ((y-5)2 )
D ((y-25)2 )
Explanation opens after your attempt
Correct Answer
C. ((y-5)2 )
Step 1
Concept
\(25=5^2\) and \(-10y=-2\cdot5y\). So (y-2 -10y+25=(y-5)2 ).
Step 2
Why this answer is correct
The correct answer is C. ((y-5)2 ). \(25=5^2\) and \(-10y=-2\cdot5y\). So (y-2 -10y+25=(y-5)2 ).
Step 3
Exam Tip
\(25=5^2\) और \(-10y=-2\cdot5y\) है। इसलिए (y-2 -10y+25=(y-5)2 ) है।
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\(p^2-q^2\) का सही गुणनखंडन चुनिए।
Choose the correct factorisation of \(p^2-q^2\).
#difference of squares
#general identity
#factorisation
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A ((p+q)2 )
B ((p-q)2 )
C (p(p-q))
D ((p-q)(p+q))
Explanation opens after your attempt
Correct Answer
D. ((p-q)(p+q))
Step 1
Concept
This is a difference of squares. Therefore (p-2 -q-2 =(p-q)(p+q)).
Step 2
Why this answer is correct
The correct answer is D. ((p-q)(p+q)). This is a difference of squares. Therefore (p-2 -q-2 =(p-q)(p+q)).
Step 3
Exam Tip
यह वर्गों का अंतर है। इसलिए (p-2 -q-2 =(p-q)(p+q)) होगा।
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(3x+3y) का गुणनखंडन क्या होगा?
What will be the factorisation of (3x+3y)?
#common factor
#two terms
#factorisation
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A (3(x+y))
B (3(x-y))
C (x(3+y))
D (y(3+x))
Explanation opens after your attempt
Correct Answer
A. (3(x+y))
Step 1
Concept
(3) is common in both terms. So (3x+3y=3(x+y)).
Step 2
Why this answer is correct
The correct answer is A. (3(x+y)). (3) is common in both terms. So (3x+3y=3(x+y)).
Step 3
Exam Tip
दोनों पदों में (3) समान है। इसलिए (3x+3y=3(x+y)) है।
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\(7a^2-14a\) में समान गुणनखंड निकालने पर क्या बचेगा?
After taking out the common factor in \(7a^2-14a\), what remains?
#monomial factor
#common factor
#factorisation
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A (7(a-2))
B (7a(a-2))
C (a(7a-14))
D (14a(a-7))
Explanation opens after your attempt
Correct Answer
B. (7a(a-2))
Step 1
Concept
(7a) is common in both terms. Therefore (7a-2 -14a=7a(a-2)).
Step 2
Why this answer is correct
The correct answer is B. (7a(a-2)). (7a) is common in both terms. Therefore (7a-2 -14a=7a(a-2)).
Step 3
Exam Tip
दोनों पदों में (7a) समान है। इसलिए (7a-2 -14a=7a(a-2)) है।
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\(x^2+5x+6\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(x^2+5x+6\)?
#quadratic factorisation
#split middle term
#easy algebra
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A ((x+1)(x+6))
B ((x+2)(x+3))
C ((x-2)(x-3))
D ((x+5)(x+6))
Explanation opens after your attempt
Correct Answer
B. ((x+2)(x+3))
Step 1
Concept
(2+3=5) and \(2\cdot3=6\). Exam tip: find two numbers whose sum gives the middle term and product gives the last term.
Step 2
Why this answer is correct
The correct answer is B. ((x+2)(x+3)). (2+3=5) and \(2\cdot3=6\). Exam tip: find two numbers whose sum gives the middle term and product gives the last term.
Step 3
Exam Tip
(2+3=5) और \(2\cdot3=6\) है। परीक्षा में ऐसे दो संख्याएं खोजें जिनका योग मध्य पद और गुणन अंतिम पद दे।
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\(x^2+7x+12\) के गुणनखंड क्या हैं?
What are the factors of \(x^2+7x+12\)?
#quadratic factors
#factorisation
#middle term
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A ((x+1)(x+12))
B ((x+2)(x+6))
C ((x+3)(x+4))
D ((x-3)(x-4))
Explanation opens after your attempt
Correct Answer
C. ((x+3)(x+4))
Step 1
Concept
(3+4=7) and \(3\cdot4=12\). Exam tip: check the sum of the factors of the last term.
Step 2
Why this answer is correct
The correct answer is C. ((x+3)(x+4)). (3+4=7) and \(3\cdot4=12\). Exam tip: check the sum of the factors of the last term.
Step 3
Exam Tip
(3+4=7) और \(3\cdot4=12\) है। परीक्षा में अंतिम पद के कारकों का योग जांचें।
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\(x^2+9x+20\) का सही गुणनखंडन चुनिए।
Choose the correct factorisation of \(x^2+9x+20\).
#quadratic factorisation
#sum product
#algebra
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A ((x+4)(x+5))
B ((x+2)(x+10))
C ((x+1)(x+20))
D ((x+3)(x+7))
Explanation opens after your attempt
Correct Answer
A. ((x+4)(x+5))
Step 1
Concept
(4+5=9) and \(4\cdot5=20\). Exam tip: correct factors must satisfy both conditions.
Step 2
Why this answer is correct
The correct answer is A. ((x+4)(x+5)). (4+5=9) and \(4\cdot5=20\). Exam tip: correct factors must satisfy both conditions.
Step 3
Exam Tip
(4+5=9) और \(4\cdot5=20\) है। परीक्षा में सही कारक वही होंगे जिनसे दोनों शर्तें पूरी हों।
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\(x^2+8x+15\) का गुणनखंडन क्या है?
What is the factorisation of \(x^2+8x+15\)?
#factorisation
#quadratic trinomial
#sum product
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A ((x+1)(x+15))
B ((x+3)(x+5))
C ((x+2)(x+6))
D ((x+4)(x+4))
Explanation opens after your attempt
Correct Answer
B. ((x+3)(x+5))
Step 1
Concept
(3+5=8) and \(3\cdot5=15\). Exam tip: start with smaller factors.
Step 2
Why this answer is correct
The correct answer is B. ((x+3)(x+5)). (3+5=8) and \(3\cdot5=15\). Exam tip: start with smaller factors.
Step 3
Exam Tip
(3+5=8) और \(3\cdot5=15\) है। परीक्षा में छोटे कारकों से शुरुआत करें।
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\(x^2-25\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(x^2-25\)?
#difference of squares
#factorisation
#identity
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A ((x-25)(x+25))
B ((x+5)2 )
C ((x-5)(x+5))
D ((x-5)2 )
Explanation opens after your attempt
Correct Answer
C. ((x-5)(x+5))
Step 1
Concept
\(25=5^2\) and this is a difference of squares. Therefore (x-2 -25=(x-5)(x+5)).
Step 2
Why this answer is correct
The correct answer is C. ((x-5)(x+5)). \(25=5^2\) and this is a difference of squares. Therefore (x-2 -25=(x-5)(x+5)).
Step 3
Exam Tip
\(25=5^2\) है और यह वर्गों का अंतर है। इसलिए (x-2 -25=(x-5)(x+5)) होगा।
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\(9x^2-1\) का सही गुणनखंडन क्या है?
What is the correct factorisation of \(9x^2-1\)?
#difference of squares
#coefficient
#factorisation
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A ((3x-1)2 )
B ((9x-1)(x+1))
C ((3x+1)2 )
D ((3x-1)(3x+1))
Explanation opens after your attempt
Correct Answer
D. ((3x-1)(3x+1))
Step 1
Concept
(9x-2 =(3x)2 ) and \(1=1^2\). So the difference of squares becomes ((3x-1)(3x+1)).
Step 2
Why this answer is correct
The correct answer is D. ((3x-1)(3x+1)). (9x-2 =(3x)2 ) and \(1=1^2\). So the difference of squares becomes ((3x-1)(3x+1)).
Step 3
Exam Tip
(9x-2 =(3x)2 ) और \(1=1^2\) है। इसलिए वर्गों का अंतर ((3x-1)(3x+1)) बनेगा।
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(2x+6) में (2) समान निकालने पर क्या मिलेगा?
What is obtained after taking (2) common from (2x+6)?
#common factor
#basic factorisation
#linear expression
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A (2(x+3))
B (2(x+6))
C (x(2+6))
D (6(x+2))
Explanation opens after your attempt
Correct Answer
A. (2(x+3))
Step 1
Concept
\(2x\div2=x\) and \(6\div2=3\). Therefore (2x+6=2(x+3)).
Step 2
Why this answer is correct
The correct answer is A. (2(x+3)). \(2x\div2=x\) and \(6\div2=3\). Therefore (2x+6=2(x+3)).
Step 3
Exam Tip
\(2x\div2=x\) और \(6\div2=3\) है। इसलिए (2x+6=2(x+3)) है।
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(15p+20q) का सबसे बड़ा समान संख्यात्मक गुणनखंड क्या है?
What is the greatest common numerical factor of (15p+20q)?
#hcf
#common factor
#factorisation
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A (10)
B (5)
C (15)
D (20)
Explanation opens after your attempt
Step 1
Concept
The greatest common factor of (15) and (20) is (5). Exam tip: first find the HCF of the numbers.
Step 2
Why this answer is correct
The correct answer is B. (5). The greatest common factor of (15) and (20) is (5). Exam tip: first find the HCF of the numbers.
Step 3
Exam Tip
(15) और (20) का सबसे बड़ा समान गुणनखंड (5) है। परीक्षा में संख्याओं का महत्तम समापवर्तक पहले निकालें।
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(15p+20q) का गुणनखंडन क्या होगा?
What will be the factorisation of (15p+20q)?
#common factor
#hcf
#algebraic expression
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A (5(3p+4q))
B (10(p+q))
C (15(p+20q))
D (20(15p+q))
Explanation opens after your attempt
Correct Answer
A. (5(3p+4q))
Step 1
Concept
(5) is common in both terms. So (15p+20q=5(3p+4q)).
Step 2
Why this answer is correct
The correct answer is A. (5(3p+4q)). (5) is common in both terms. So (15p+20q=5(3p+4q)).
Step 3
Exam Tip
दोनों पदों में (5) समान है। इसलिए (15p+20q=5(3p+4q)) होगा।
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\(x^2+4x+4\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(x^2+4x+4\)?
#perfect square
#factorisation
#binomial
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A ((x+4)2 )
B ((x+2)2 )
C ((x-2)2 )
D ((x+1)(x+4))
Explanation opens after your attempt
Correct Answer
B. ((x+2)2 )
Step 1
Concept
\(4=2^2\) and \(4x=2\cdot2x\). Therefore (x-2 +4x+4=(x+2)2 ).
Step 2
Why this answer is correct
The correct answer is B. ((x+2)2 ). \(4=2^2\) and \(4x=2\cdot2x\). Therefore (x-2 +4x+4=(x+2)2 ).
Step 3
Exam Tip
\(4=2^2\) और \(4x=2\cdot2x\) है। इसलिए (x-2 +4x+4=(x+2)2 ) है।
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\(x^2-6x+9\) का सही गुणनखंडन चुनिए।
Choose the correct factorisation of \(x^2-6x+9\).
#perfect square
#negative middle term
#factorisation
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A ((x+3)2 )
B ((x-6)2 )
C ((x-3)2 )
D ((x-9)2 )
Explanation opens after your attempt
Correct Answer
C. ((x-3)2 )
Step 1
Concept
\(9=3^2\) and \(-6x=-2\cdot3x\). Therefore it is ((x-3)2 ).
Step 2
Why this answer is correct
The correct answer is C. ((x-3)2 ). \(9=3^2\) and \(-6x=-2\cdot3x\). Therefore it is ((x-3)2 ).
Step 3
Exam Tip
\(9=3^2\) और \(-6x=-2\cdot3x\) है। इसलिए यह ((x-3)2 ) है।
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\(4x^2+12x+9\) का गुणनखंडन क्या होगा?
What will be the factorisation of \(4x^2+12x+9\)?
#perfect square
#coefficient
#factorisation
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A ((2x+9)2 )
B ((4x+3)2 )
C ((2x-3)2 )
D ((2x+3)2 )
Explanation opens after your attempt
Correct Answer
D. ((2x+3)2 )
Step 1
Concept
(4x-2 =(2x)2 ), \(9=3^2\), and \(12x=2\cdot2x\cdot3\). Exam tip: match the roots of the first and last terms.
Step 2
Why this answer is correct
The correct answer is D. ((2x+3)2 ). (4x-2 =(2x)2 ), \(9=3^2\), and \(12x=2\cdot2x\cdot3\). Exam tip: match the roots of the first and last terms.
Step 3
Exam Tip
(4x-2 =(2x)2 ), \(9=3^2\), और \(12x=2\cdot2x\cdot3\) है। परीक्षा में पहले और अंतिम पद की जड़ें मिलाएं।
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\(2a^2+4a\) का गुणनखंडन करें।
Factorise \(2a^2+4a\).
#common monomial
#factorisation
#algebra
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A (2a(a+2))
B (2\(a^2+4a\))
C (a(2a+4a))
D (4a(a+2))
Explanation opens after your attempt
Correct Answer
A. (2a(a+2))
Step 1
Concept
(2a) is common in both terms. Therefore (2a-2 +4a=2a(a+2)).
Step 2
Why this answer is correct
The correct answer is A. (2a(a+2)). (2a) is common in both terms. Therefore (2a-2 +4a=2a(a+2)).
Step 3
Exam Tip
दोनों पदों में (2a) समान है। इसलिए (2a-2 +4a=2a(a+2)) होगा।
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\(8m^2-12m\) में समान गुणनखंड निकालकर सही रूप चुनिए।
Choose the correct form after taking the common factor from \(8m^2-12m\).
#gcf
#common factor
#factorisation
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A (4m(2m-3))
B (2m(4m-12))
C (8m(m-12 ))
D (12m(8m-1))
Explanation opens after your attempt
Correct Answer
A. (4m(2m-3))
Step 1
Concept
(4m) is the greatest common factor in both terms. So (8m-2 -12m=4m(2m-3)).
Step 2
Why this answer is correct
The correct answer is A. (4m(2m-3)). (4m) is the greatest common factor in both terms. So (8m-2 -12m=4m(2m-3)).
Step 3
Exam Tip
दोनों पदों में (4m) सबसे बड़ा समान गुणनखंड है। इसलिए (8m-2 -12m=4m(2m-3)) है।
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(ab+ac+ad) का गुणनखंडन क्या है?
What is the factorisation of (ab+ac+ad)?
#three terms
#common factor
#factorisation
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A (a(b+c+d))
B (b(a+c+d))
C (abc(a+d))
D (d(a+b+c))
Explanation opens after your attempt
Correct Answer
A. (a(b+c+d))
Step 1
Concept
(a) is common in all three terms. Therefore (ab+ac+ad=a(b+c+d)).
Step 2
Why this answer is correct
The correct answer is A. (a(b+c+d)). (a) is common in all three terms. Therefore (ab+ac+ad=a(b+c+d)).
Step 3
Exam Tip
तीनों पदों में (a) समान है। इसलिए (ab+ac+ad=a(b+c+d)) है।
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\(x^2+3x+2\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(x^2+3x+2\)?
#quadratic factorisation
#easy trinomial
#factors
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A ((x+1)(x+2))
B ((x+1)(x+3))
C ((x+2)(x+2))
D ((x-1)(x-2))
Explanation opens after your attempt
Correct Answer
A. ((x+1)(x+2))
Step 1
Concept
(1+2=3) and \(1\cdot2=2\). Exam tip: in simple trinomials, check both sum and product.
Step 2
Why this answer is correct
The correct answer is A. ((x+1)(x+2)). (1+2=3) and \(1\cdot2=2\). Exam tip: in simple trinomials, check both sum and product.
Step 3
Exam Tip
(1+2=3) और \(1\cdot2=2\) है। परीक्षा में आसान त्रिपदों में योग और गुणन दोनों जांचें।
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\(x^2+10x+21\) के गुणनखंड क्या हैं?
What are the factors of \(x^2+10x+21\)?
#sum product
#quadratic factors
#factorisation
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A ((x+1)(x+21))
B ((x+3)(x+7))
C ((x+4)(x+6))
D ((x+5)(x+5))
Explanation opens after your attempt
Correct Answer
B. ((x+3)(x+7))
Step 1
Concept
(3+7=10) and \(3\cdot7=21\). Exam tip: choose the pair of factors of the last term.
Step 2
Why this answer is correct
The correct answer is B. ((x+3)(x+7)). (3+7=10) and \(3\cdot7=21\). Exam tip: choose the pair of factors of the last term.
Step 3
Exam Tip
(3+7=10) और \(3\cdot7=21\) है। परीक्षा में अंतिम पद के कारकों की जोड़ी चुनें।
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\(x^2+11x+30\) का सही गुणनखंडन चुनिए।
Choose the correct factorisation of \(x^2+11x+30\).
#quadratic trinomial
#factorisation
#sum product
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A ((x+3)(x+10))
B ((x+4)(x+7))
C ((x+5)(x+6))
D ((x+2)(x+15))
Explanation opens after your attempt
Correct Answer
C. ((x+5)(x+6))
Step 1
Concept
(5+6=11) and \(5\cdot6=30\). Exam tip: the correct pair must satisfy both conditions.
Step 2
Why this answer is correct
The correct answer is C. ((x+5)(x+6)). (5+6=11) and \(5\cdot6=30\). Exam tip: the correct pair must satisfy both conditions.
Step 3
Exam Tip
(5+6=11) और \(5\cdot6=30\) है। परीक्षा में सही जोड़ी वही है जो दोनों शर्तें पूरी करे।
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\(x^2-4x+4\) किसका गुणनखंड रूप है?
What is the factor form of \(x^2-4x+4\)?
#perfect square
#minus sign
#factorisation
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A ((x+2)2 )
B ((x-4)2 )
C ((x+4)2 )
D ((x-2)2 )
Explanation opens after your attempt
Correct Answer
D. ((x-2)2 )
Step 1
Concept
\(4=2^2\) and \(-4x=-2\cdot2x\). Therefore it is ((x-2)2 ).
Step 2
Why this answer is correct
The correct answer is D. ((x-2)2 ). \(4=2^2\) and \(-4x=-2\cdot2x\). Therefore it is ((x-2)2 ).
Step 3
Exam Tip
\(4=2^2\) और \(-4x=-2\cdot2x\) है। इसलिए यह ((x-2)2 ) है।
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\(a^2-b^2\) के गुणनखंडों में कौन से चिह्न आते हैं?
Which signs appear in the factors of \(a^2-b^2\)?
#difference of squares
#signs
#factorisation
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A दोनों धन / Both positive
B दोनों ऋण / Both negative
C एक अंतर और एक योग / One difference and one sum
D केवल गुणा चिह्न / Only multiplication sign
Explanation opens after your attempt
Correct Answer
C. एक अंतर और एक योग / One difference and one sum
Step 1
Concept
(a-2 -b-2 =(a-b)(a+b)). Exam tip: write minus in one bracket and plus in the other.
Step 2
Why this answer is correct
The correct answer is C. एक अंतर और एक योग / One difference and one sum. (a-2 -b-2 =(a-b)(a+b)). Exam tip: write minus in one bracket and plus in the other.
Step 3
Exam Tip
(a-2 -b-2 =(a-b)(a+b)) होता है। परीक्षा में एक कोष्ठक में ऋण और दूसरे में धन लिखें।
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\(16a^2-25b^2\) का गुणनखंडन क्या होगा?
What will be the factorisation of \(16a^2-25b^2\)?
#difference of squares
#coefficient
#factorisation
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A ((4a+5b)2 )
B ((4a-5b)2 )
C ((4a-5b)(4a+5b))
D (16\(a^2-25b^2\))
Explanation opens after your attempt
Correct Answer
C. ((4a-5b)(4a+5b))
Step 1
Concept
(16a-2 =(4a)2 ) and (25b-2 =(5b)2 ). So use difference of squares.
Step 2
Why this answer is correct
The correct answer is C. ((4a-5b)(4a+5b)). (16a-2 =(4a)2 ) and (25b-2 =(5b)2 ). So use difference of squares.
Step 3
Exam Tip
(16a-2 =(4a)2 ) और (25b-2 =(5b)2 ) है। इसलिए वर्गों के अंतर का उपयोग करें।
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\(x^2+2xy+y^2\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(x^2+2xy+y^2\)?
#perfect square
#two variables
#factorisation
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A ((x+y)2 )
B ((x-y)2 )
C ((x+y)(x-y))
D (x(x+2y))
Explanation opens after your attempt
Correct Answer
A. ((x+y)2 )
Step 1
Concept
This is a perfect square trinomial. Therefore (x-2 +2xy+y-2 =(x+y)2 ).
Step 2
Why this answer is correct
The correct answer is A. ((x+y)2 ). This is a perfect square trinomial. Therefore (x-2 +2xy+y-2 =(x+y)2 ).
Step 3
Exam Tip
यह पूर्ण वर्ग त्रिपद है। इसलिए (x-2 +2xy+y-2 =(x+y)2 ) है।
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\(x^2-2xy+y^2\) का सही गुणनखंडन चुनिए।
Choose the correct factorisation of \(x^2-2xy+y^2\).
#perfect square
#negative middle term
#factorisation
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A ((x+y)2 )
B ((x-y)2 )
C ((x+y)(x-y))
D (y(x-2x+y))
Explanation opens after your attempt
Correct Answer
B. ((x-y)2 )
Step 1
Concept
The middle term is negative, so it is a subtraction perfect square. (x-2 -2xy+y-2 =(x-y)2 ).
Step 2
Why this answer is correct
The correct answer is B. ((x-y)2 ). The middle term is negative, so it is a subtraction perfect square. (x-2 -2xy+y-2 =(x-y)2 ).
Step 3
Exam Tip
मध्य पद ऋण है इसलिए यह घटाव वाला पूर्ण वर्ग है। (x-2 -2xy+y-2 =(x-y)2 ) होगा।
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\(3x^2+6x+3\) में पहले कौन सा समान गुणनखंड निकालना चाहिए?
Which common factor should be taken out first from \(3x^2+6x+3\)?
#common factor
#three terms
#factorisation
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A (3)
B (x)
C (6)
D (3x)
Explanation opens after your attempt
Step 1
Concept
(3) is common in all three terms. Exam tip: taking out the common factor first makes further factorisation easier.
Step 2
Why this answer is correct
The correct answer is A. (3). (3) is common in all three terms. Exam tip: taking out the common factor first makes further factorisation easier.
Step 3
Exam Tip
तीनों पदों में (3) समान है। परीक्षा में पहले समान गुणनखंड निकालने से आगे का गुणनखंडन सरल होता है।
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\(3x^2+6x+3\) का पूर्ण गुणनखंडन क्या है?
What is the complete factorisation of \(3x^2+6x+3\)?
#complete factorisation
#common factor
#perfect square
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A (3(x+1)2 )
B (3(x+2)2 )
C ((3x+1)2 )
D (3(x-1)2 )
Explanation opens after your attempt
Correct Answer
A. (3(x+1)2 )
Step 1
Concept
First take (3) common and write (x-2 +2x+1=(x+1)2 ). Exam tip: continue until complete factorisation.
Step 2
Why this answer is correct
The correct answer is A. (3(x+1)2 ). First take (3) common and write (x-2 +2x+1=(x+1)2 ). Exam tip: continue until complete factorisation.
Step 3
Exam Tip
पहले (3) समान निकालें और (x-2 +2x+1=(x+1)2 ) लिखें। परीक्षा में पूर्ण गुणनखंडन तक रुकें नहीं।
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\(a^2+5a\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(a^2+5a\)?
#common variable
#factorisation
#binomial
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A (a(a+5))
B (5(a+5))
C (a-2 (1+5))
D ((a+5)2 )
Explanation opens after your attempt
Correct Answer
A. (a(a+5))
Step 1
Concept
(a) is common in both terms. Therefore (a-2 +5a=a(a+5)).
Step 2
Why this answer is correct
The correct answer is A. (a(a+5)). (a) is common in both terms. Therefore (a-2 +5a=a(a+5)).
Step 3
Exam Tip
दोनों पदों में (a) समान है। इसलिए (a-2 +5a=a(a+5)) है।
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\(m^2-6m\) का सही गुणनखंडन चुनिए।
Choose the correct factorisation of \(m^2-6m\).
#common factor
#negative term
#factorisation
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A (m(m+6))
B (m(m-6 ))
C (6(m-1 ))
D ((m-6 )2 )
Explanation opens after your attempt
Correct Answer
B. (m(m-6 ))
Step 1
Concept
(m) is common in both terms and the second term is negative. So (m-2 -6m=m(m-6 )).
Step 2
Why this answer is correct
The correct answer is B. (m(m-6 )). (m) is common in both terms and the second term is negative. So (m-2 -6m=m(m-6 )).
Step 3
Exam Tip
दोनों पदों में (m) समान है और दूसरा पद ऋण है। इसलिए (m-2 -6m=m(m-6 )) है।
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(6xy+9xz) का गुणनखंडन क्या है?
What is the factorisation of (6xy+9xz)?
#common factor
#multiple variables
#factorisation
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A (3x(2y+3z))
B (3(2xy+9xz))
C (x(6y+9z))
D (9x(6y+z))
Explanation opens after your attempt
Correct Answer
A. (3x(2y+3z))
Step 1
Concept
(3x) is common in both terms. Therefore (6xy+9xz=3x(2y+3z)).
Step 2
Why this answer is correct
The correct answer is A. (3x(2y+3z)). (3x) is common in both terms. Therefore (6xy+9xz=3x(2y+3z)).
Step 3
Exam Tip
दोनों पदों में (3x) समान है। इसलिए (6xy+9xz=3x(2y+3z)) होगा।
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\(x^2+13x+36\) के गुणनखंड कौन से हैं?
What are the factors of \(x^2+13x+36\)?
#quadratic factorisation
#factors
#sum product
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A ((x+1)(x+36))
B ((x+2)(x+18))
C ((x+3)(x+12))
D ((x+4)(x+9))
Explanation opens after your attempt
Correct Answer
D. ((x+4)(x+9))
Step 1
Concept
(4+9=13) and \(4\cdot9=36\). Exam tip: mentally check all factors of the last term.
Step 2
Why this answer is correct
The correct answer is D. ((x+4)(x+9)). (4+9=13) and \(4\cdot9=36\). Exam tip: mentally check all factors of the last term.
Step 3
Exam Tip
(4+9=13) और \(4\cdot9=36\) है। परीक्षा में अंतिम पद के सभी कारक मन में जांचें।
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\(x^2+12x+36\) का गुणनखंड रूप क्या है?
What is the factor form of \(x^2+12x+36\)?
#perfect square
#factor form
#identity
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A ((x+6)2 )
B ((x+12)2 )
C ((x-6)2 )
D ((x+3)(x+12))
Explanation opens after your attempt
Correct Answer
A. ((x+6)2 )
Step 1
Concept
\(36=6^2\) and \(12x=2\cdot6x\). Therefore it is ((x+6)2 ).
Step 2
Why this answer is correct
The correct answer is A. ((x+6)2 ). \(36=6^2\) and \(12x=2\cdot6x\). Therefore it is ((x+6)2 ).
Step 3
Exam Tip
\(36=6^2\) और \(12x=2\cdot6x\) है। इसलिए यह ((x+6)2 ) है।
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\(x^2-81\) का गुणनखंडन क्या होगा?
What will be the factorisation of \(x^2-81\)?
#difference of squares
#factorisation
#square number
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A ((x-9)(x+9))
B ((x+81)(x-81))
C ((x-9)2 )
D ((x+9)2 )
Explanation opens after your attempt
Correct Answer
A. ((x-9)(x+9))
Step 1
Concept
\(81=9^2\) and \(x^2-81\) is a difference of squares. So ((x-9)(x+9)) is obtained.
Step 2
Why this answer is correct
The correct answer is A. ((x-9)(x+9)). \(81=9^2\) and \(x^2-81\) is a difference of squares. So ((x-9)(x+9)) is obtained.
Step 3
Exam Tip
\(81=9^2\) है और \(x^2-81\) वर्गों का अंतर है। इसलिए ((x-9)(x+9)) मिलेगा।
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\(25x^2-36\) का सही गुणनखंडन चुनिए।
Choose the correct factorisation of \(25x^2-36\).
#difference of squares
#coefficient
#factorisation
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A ((5x-6)2 )
B ((5x-6)(5x+6))
C ((25x-36)(x+1))
D ((5x+6)2 )
Explanation opens after your attempt
Correct Answer
B. ((5x-6)(5x+6))
Step 1
Concept
(25x-2 =(5x)2 ) and \(36=6^2\). Difference of squares gives ((5x-6)(5x+6)).
Step 2
Why this answer is correct
The correct answer is B. ((5x-6)(5x+6)). (25x-2 =(5x)2 ) and \(36=6^2\). Difference of squares gives ((5x-6)(5x+6)).
Step 3
Exam Tip
(25x-2 =(5x)2 ) और \(36=6^2\) है। वर्गों के अंतर से ((5x-6)(5x+6)) बनता है।
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\(2x^2+10x\) का गुणनखंडन क्या है?
What is the factorisation of \(2x^2+10x\)?
#common factor
#monomial
#factorisation
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A (2x(x+5))
B (2\(x^2+10x\))
C (10x(2x+1))
D (x(2x+10x))
Explanation opens after your attempt
Correct Answer
A. (2x(x+5))
Step 1
Concept
(2x) is common in both terms. Therefore (2x-2 +10x=2x(x+5)).
Step 2
Why this answer is correct
The correct answer is A. (2x(x+5)). (2x) is common in both terms. Therefore (2x-2 +10x=2x(x+5)).
Step 3
Exam Tip
दोनों पदों में (2x) समान है। इसलिए (2x-2 +10x=2x(x+5)) है।
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\(x^2+14x+49\) का गुणनखंडन चुनिए।
Choose the factorisation of \(x^2+14x+49\).
#perfect square
#binomial factorisation
#identity
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A ((x+14)2 )
B ((x+7)2 )
C ((x-7)2 )
D ((x+1)(x+49))
Explanation opens after your attempt
Correct Answer
B. ((x+7)2 )
Step 1
Concept
\(49=7^2\) and \(14x=2\cdot7x\). So (x-2 +14x+49=(x+7)2 ).
Step 2
Why this answer is correct
The correct answer is B. ((x+7)2 ). \(49=7^2\) and \(14x=2\cdot7x\). So (x-2 +14x+49=(x+7)2 ).
Step 3
Exam Tip
\(49=7^2\) और \(14x=2\cdot7x\) है। इसलिए (x-2 +14x+49=(x+7)2 ) है।
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\(x^2+6x+8\) का गुणनखंडन कौन सा है?
Which is the factorisation of \(x^2+6x+8\)?
#quadratic factorisation
#sum product
#factors
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A ((x+1)(x+8))
B ((x+2)(x+4))
C ((x+3)(x+3))
D ((x-2)(x-4))
Explanation opens after your attempt
Correct Answer
B. ((x+2)(x+4))
Step 1
Concept
(2+4=6) and \(2\cdot4=8\). Exam tip: match both the middle term and the last term.
Step 2
Why this answer is correct
The correct answer is B. ((x+2)(x+4)). (2+4=6) and \(2\cdot4=8\). Exam tip: match both the middle term and the last term.
Step 3
Exam Tip
(2+4=6) और \(2\cdot4=8\) है। परीक्षा में मध्य पद और अंतिम पद दोनों से मिलान करें।
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\(4x^2-12x+9\) का सही गुणनखंडन क्या है?
What is the correct factorisation of \(4x^2-12x+9\)?
#perfect square
#negative middle
#factorisation
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A ((2x+3)2 )
B ((4x-9)2 )
C ((2x-3)2 )
D ((2x-9)2 )
Explanation opens after your attempt
Correct Answer
C. ((2x-3)2 )
Step 1
Concept
(4x-2 =(2x)2 ), \(9=3^2\), and the middle term is (-12x). Therefore ((2x-3)2 ) is correct.
Step 2
Why this answer is correct
The correct answer is C. ((2x-3)2 ). (4x-2 =(2x)2 ), \(9=3^2\), and the middle term is (-12x). Therefore ((2x-3)2 ) is correct.
Step 3
Exam Tip
(4x-2 =(2x)2 ), \(9=3^2\), और मध्य पद (-12x) है। इसलिए ((2x-3)2 ) सही है।
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