(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)
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Explanation
Simple Explanation
(6x) और (9) दोनों में (3) समान है। परीक्षा में पहले संख्यात्मक समान गुणनखंड देखें। / (3) is common in both (6x) and (9). Exam tip: first look for the numerical common factor.
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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))
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Correct Answer
B. (4(a+2))
Explanation
Simple Explanation
दोनों पदों में (4) समान है और (4a+8=4(a+2)) है। परीक्षा में बाहर निकाले गए गुणनखंड को दोबारा गुणा करके जांचें। / (4) is common in both terms and (4a+8=4(a+2)). Exam tip: multiply back the factor taken out to check.
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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)
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Explanation
Simple Explanation
दोनों पदों में (x) समान है। इसलिए (xy+xz=x(y+z)) होगा। / (x) is common in both terms. Therefore (xy+xz=x(y+z)).
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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 ))
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Correct Answer
D. (5(m-3 ))
Explanation
Simple Explanation
दोनों पदों में (5) समान है और \(15\div5=3\) है। परीक्षा में ऋण चिह्न को कोष्ठक के अंदर सही रखें। / (5) is common in both terms and \(15\div5=3\). Exam tip: keep the negative sign correctly inside the bracket.
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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))
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Correct Answer
A. (a(a+b))
Explanation
Simple Explanation
दोनों पदों में (a) समान है। इसलिए (a-2 +ab=a(a+b)) है। / (a) is common in both terms. So (a-2 +ab=a(a+b)).
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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)
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Explanation
Simple Explanation
संख्याओं में (6) और दोनों पदों में (x) समान है। इसलिए समान गुणनखंड (6x) है। / (6) is common in the numbers and (x) is common in both terms. So the common factor is (6x).
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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)
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Correct Answer
C. (a-2 -b-2 =(a-b)(a+b))
Explanation
Simple Explanation
\(x^2-9=x^2-3^2\) है इसलिए वर्गों के अंतर की पहचान लगेगी। परीक्षा में दोनों पदों को वर्ग के रूप में पहचानें। / \(x^2-9=x^2-3^2\), so the difference of squares identity is used. Exam tip: identify both terms as squares.
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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))
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Correct Answer
D. ((x-4)(x+4))
Explanation
Simple Explanation
\(16=4^2\) है इसलिए (x-2 -16=(x-4)(x+4)) होगा। परीक्षा में वर्गों के अंतर में योग और अंतर दोनों कारक लिखें। / \(16=4^2\), so (x-2 -16=(x-4)(x+4)). Exam tip: in difference of squares, write both sum and difference factors.
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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))
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Correct Answer
A. ((a+b)2 )
Explanation
Simple Explanation
यह पूर्ण वर्ग त्रिपद है क्योंकि बीच का पद (2ab) है। परीक्षा में पहले और अंतिम पदों की जड़ें देखें। / This is a perfect square trinomial because the middle term is (2ab). Exam tip: check the roots of the first and last terms.
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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)
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Explanation
Simple Explanation
\(9=3^2\) और \(6x=2\cdot3x\) है। इसलिए यह ((x+3)2 ) है। / \(9=3^2\) and \(6x=2\cdot3x\). Therefore it is ((x+3)2 ).
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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 )
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Correct Answer
C. ((y-5)2 )
Explanation
Simple Explanation
\(25=5^2\) और \(-10y=-2\cdot5y\) है। इसलिए (y-2 -10y+25=(y-5)2 ) है। / \(25=5^2\) and \(-10y=-2\cdot5y\). So (y-2 -10y+25=(y-5)2 ).
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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))
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Correct Answer
D. ((p-q)(p+q))
Explanation
Simple Explanation
यह वर्गों का अंतर है। इसलिए (p-2 -q-2 =(p-q)(p+q)) होगा। / This is a difference of squares. Therefore (p-2 -q-2 =(p-q)(p+q)).
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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))
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Correct Answer
A. (3(x+y))
Explanation
Simple Explanation
दोनों पदों में (3) समान है। इसलिए (3x+3y=3(x+y)) है। / (3) is common in both terms. So (3x+3y=3(x+y)).
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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))
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Correct Answer
B. (7a(a-2))
Explanation
Simple Explanation
दोनों पदों में (7a) समान है। इसलिए (7a-2 -14a=7a(a-2)) है। / (7a) is common in both terms. Therefore (7a-2 -14a=7a(a-2)).
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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))
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Correct Answer
B. ((x+2)(x+3))
Explanation
Simple Explanation
(2+3=5) और \(2\cdot3=6\) है। परीक्षा में ऐसे दो संख्याएं खोजें जिनका योग मध्य पद और गुणन अंतिम पद दे। / (2+3=5) and \(2\cdot3=6\). Exam tip: find two numbers whose sum gives the middle term and product gives the last term.
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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))
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Correct Answer
C. ((x+3)(x+4))
Explanation
Simple Explanation
(3+4=7) और \(3\cdot4=12\) है। परीक्षा में अंतिम पद के कारकों का योग जांचें। / (3+4=7) and \(3\cdot4=12\). Exam tip: check the sum of the factors of the last term.
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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))
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Correct Answer
A. ((x+4)(x+5))
Explanation
Simple Explanation
(4+5=9) और \(4\cdot5=20\) है। परीक्षा में सही कारक वही होंगे जिनसे दोनों शर्तें पूरी हों। / (4+5=9) and \(4\cdot5=20\). Exam tip: correct factors must satisfy both conditions.
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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))
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Correct Answer
B. ((x+3)(x+5))
Explanation
Simple Explanation
(3+5=8) और \(3\cdot5=15\) है। परीक्षा में छोटे कारकों से शुरुआत करें। / (3+5=8) and \(3\cdot5=15\). Exam tip: start with smaller factors.
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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 )
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Correct Answer
C. ((x-5)(x+5))
Explanation
Simple Explanation
\(25=5^2\) है और यह वर्गों का अंतर है। इसलिए (x-2 -25=(x-5)(x+5)) होगा। / \(25=5^2\) and this is a difference of squares. Therefore (x-2 -25=(x-5)(x+5)).
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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))
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Correct Answer
D. ((3x-1)(3x+1))
Explanation
Simple Explanation
(9x-2 =(3x)2 ) और \(1=1^2\) है। इसलिए वर्गों का अंतर ((3x-1)(3x+1)) बनेगा। / (9x-2 =(3x)2 ) and \(1=1^2\). So the difference of squares becomes ((3x-1)(3x+1)).
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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))
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Correct Answer
A. (2(x+3))
Explanation
Simple Explanation
\(2x\div2=x\) और \(6\div2=3\) है। इसलिए (2x+6=2(x+3)) है। / \(2x\div2=x\) and \(6\div2=3\). Therefore (2x+6=2(x+3)).
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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)
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Explanation
Simple Explanation
(15) और (20) का सबसे बड़ा समान गुणनखंड (5) है। परीक्षा में संख्याओं का महत्तम समापवर्तक पहले निकालें। / The greatest common factor of (15) and (20) is (5). Exam tip: first find the HCF of the numbers.
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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))
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Correct Answer
A. (5(3p+4q))
Explanation
Simple Explanation
दोनों पदों में (5) समान है। इसलिए (15p+20q=5(3p+4q)) होगा। / (5) is common in both terms. So (15p+20q=5(3p+4q)).
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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))
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Correct Answer
B. ((x+2)2 )
Explanation
Simple Explanation
\(4=2^2\) और \(4x=2\cdot2x\) है। इसलिए (x-2 +4x+4=(x+2)2 ) है। / \(4=2^2\) and \(4x=2\cdot2x\). Therefore (x-2 +4x+4=(x+2)2 ).
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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 )
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Correct Answer
C. ((x-3)2 )
Explanation
Simple Explanation
\(9=3^2\) और \(-6x=-2\cdot3x\) है। इसलिए यह ((x-3)2 ) है। / \(9=3^2\) and \(-6x=-2\cdot3x\). Therefore it is ((x-3)2 ).
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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 )
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Correct Answer
D. ((2x+3)2 )
Explanation
Simple Explanation
(4x-2 =(2x)2 ), \(9=3^2\), और \(12x=2\cdot2x\cdot3\) है। परीक्षा में पहले और अंतिम पद की जड़ें मिलाएं। / (4x-2 =(2x)2 ), \(9=3^2\), and \(12x=2\cdot2x\cdot3\). Exam tip: match the roots of the first and last terms.
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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))
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Correct Answer
A. (2a(a+2))
Explanation
Simple Explanation
दोनों पदों में (2a) समान है। इसलिए (2a-2 +4a=2a(a+2)) होगा। / (2a) is common in both terms. Therefore (2a-2 +4a=2a(a+2)).
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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))
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Correct Answer
A. (4m(2m-3))
Explanation
Simple Explanation
दोनों पदों में (4m) सबसे बड़ा समान गुणनखंड है। इसलिए (8m-2 -12m=4m(2m-3)) है। / (4m) is the greatest common factor in both terms. So (8m-2 -12m=4m(2m-3)).
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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))
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Correct Answer
A. (a(b+c+d))
Explanation
Simple Explanation
तीनों पदों में (a) समान है। इसलिए (ab+ac+ad=a(b+c+d)) है। / (a) is common in all three terms. Therefore (ab+ac+ad=a(b+c+d)).
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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))
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Correct Answer
A. ((x+1)(x+2))
Explanation
Simple Explanation
(1+2=3) और \(1\cdot2=2\) है। परीक्षा में आसान त्रिपदों में योग और गुणन दोनों जांचें। / (1+2=3) and \(1\cdot2=2\). Exam tip: in simple trinomials, check both sum and product.
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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))
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Correct Answer
B. ((x+3)(x+7))
Explanation
Simple Explanation
(3+7=10) और \(3\cdot7=21\) है। परीक्षा में अंतिम पद के कारकों की जोड़ी चुनें। / (3+7=10) and \(3\cdot7=21\). Exam tip: choose the pair of factors of the last term.
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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))
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Correct Answer
C. ((x+5)(x+6))
Explanation
Simple Explanation
(5+6=11) और \(5\cdot6=30\) है। परीक्षा में सही जोड़ी वही है जो दोनों शर्तें पूरी करे। / (5+6=11) and \(5\cdot6=30\). Exam tip: the correct pair must satisfy both conditions.
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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 )
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Correct Answer
D. ((x-2)2 )
Explanation
Simple Explanation
\(4=2^2\) और \(-4x=-2\cdot2x\) है। इसलिए यह ((x-2)2 ) है। / \(4=2^2\) and \(-4x=-2\cdot2x\). Therefore it is ((x-2)2 ).
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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
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Correct Answer
C. एक अंतर और एक योग / One difference and one sum
Explanation
Simple Explanation
(a-2 -b-2 =(a-b)(a+b)) होता है। परीक्षा में एक कोष्ठक में ऋण और दूसरे में धन लिखें। / (a-2 -b-2 =(a-b)(a+b)). Exam tip: write minus in one bracket and plus in the other.
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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\(a^2-25b^2\))
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Correct Answer
C. ((4a-5b)(4a+5b))
Explanation
Simple Explanation
(16a-2 =(4a)2 ) और (25b-2 =(5b)2 ) है। इसलिए वर्गों के अंतर का उपयोग करें। / (16a-2 =(4a)2 ) and (25b-2 =(5b)2 ). So use difference of squares.
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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))
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Correct Answer
A. ((x+y)2 )
Explanation
Simple Explanation
यह पूर्ण वर्ग त्रिपद है। इसलिए (x-2 +2xy+y-2 =(x+y)2 ) है। / This is a perfect square trinomial. Therefore (x-2 +2xy+y-2 =(x+y)2 ).
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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))
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Correct Answer
B. ((x-y)2 )
Explanation
Simple Explanation
मध्य पद ऋण है इसलिए यह घटाव वाला पूर्ण वर्ग है। (x-2 -2xy+y-2 =(x-y)2 ) होगा। / The middle term is negative, so it is a subtraction perfect square. (x-2 -2xy+y-2 =(x-y)2 ).
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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)
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Explanation
Simple Explanation
तीनों पदों में (3) समान है। परीक्षा में पहले समान गुणनखंड निकालने से आगे का गुणनखंडन सरल होता है। / (3) is common in all three terms. Exam tip: taking out the common factor first makes further factorisation easier.
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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 )
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Correct Answer
A. (3(x+1)2 )
Explanation
Simple Explanation
पहले (3) समान निकालें और (x-2 +2x+1=(x+1)2 ) लिखें। परीक्षा में पूर्ण गुणनखंडन तक रुकें नहीं। / First take (3) common and write (x-2 +2x+1=(x+1)2 ). Exam tip: continue until complete factorisation.
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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 )
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Correct Answer
A. (a(a+5))
Explanation
Simple Explanation
दोनों पदों में (a) समान है। इसलिए (a-2 +5a=a(a+5)) है। / (a) is common in both terms. Therefore (a-2 +5a=a(a+5)).
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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 )
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Correct Answer
B. (m(m-6 ))
Explanation
Simple Explanation
दोनों पदों में (m) समान है और दूसरा पद ऋण है। इसलिए (m-2 -6m=m(m-6 )) है। / (m) is common in both terms and the second term is negative. So (m-2 -6m=m(m-6 )).
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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))
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Correct Answer
A. (3x(2y+3z))
Explanation
Simple Explanation
दोनों पदों में (3x) समान है। इसलिए (6xy+9xz=3x(2y+3z)) होगा। / (3x) is common in both terms. Therefore (6xy+9xz=3x(2y+3z)).
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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))
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Correct Answer
D. ((x+4)(x+9))
Explanation
Simple Explanation
(4+9=13) और \(4\cdot9=36\) है। परीक्षा में अंतिम पद के सभी कारक मन में जांचें। / (4+9=13) and \(4\cdot9=36\). Exam tip: mentally check all factors of the last term.
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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))
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Correct Answer
A. ((x+6)2 )
Explanation
Simple Explanation
\(36=6^2\) और \(12x=2\cdot6x\) है। इसलिए यह ((x+6)2 ) है। / \(36=6^2\) and \(12x=2\cdot6x\). Therefore it is ((x+6)2 ).
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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 )
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Correct Answer
A. ((x-9)(x+9))
Explanation
Simple Explanation
\(81=9^2\) है और \(x^2-81\) वर्गों का अंतर है। इसलिए ((x-9)(x+9)) मिलेगा। / \(81=9^2\) and \(x^2-81\) is a difference of squares. So ((x-9)(x+9)) is obtained.
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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))
Explanation
Simple Explanation
(25x-2 =(5x)2 ) और \(36=6^2\) है। वर्गों के अंतर से ((5x-6)(5x+6)) बनता है। / (25x-2 =(5x)2 ) and \(36=6^2\). Difference of squares gives ((5x-6)(5x+6)).
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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))
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Correct Answer
A. (2x(x+5))
Explanation
Simple Explanation
दोनों पदों में (2x) समान है। इसलिए (2x-2 +10x=2x(x+5)) है। / (2x) is common in both terms. Therefore (2x-2 +10x=2x(x+5)).
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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 )
Explanation
Simple Explanation
\(49=7^2\) और \(14x=2\cdot7x\) है। इसलिए (x-2 +14x+49=(x+7)2 ) है। / \(49=7^2\) and \(14x=2\cdot7x\). So (x-2 +14x+49=(x+7)2 ).
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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))
Explanation
Simple Explanation
(2+4=6) और \(2\cdot4=8\) है। परीक्षा में मध्य पद और अंतिम पद दोनों से मिलान करें। / (2+4=6) and \(2\cdot4=8\). Exam tip: match both the middle term and the last term.
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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 )
Explanation
Simple Explanation
(4x-2 =(2x)2 ), \(9=3^2\), और मध्य पद (-12x) है। इसलिए ((2x-3)2 ) सही है। / (4x-2 =(2x)2 ), \(9=3^2\), and the middle term is (-12x). Therefore ((2x-3)2 ) is correct.
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