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\(2x^2+7xy+3y^2\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(2x^2+7xy+3y^2\)?
#quadratic in two variables
#middle term
#factorisation
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A ( (2x+3y)(x+y) )
B ( (2x+y)(x+3y) )
C ( (x+2y)(2x+3y) )
D ( (2x-y)(x-3y) )
Explanation opens after your attempt
Correct Answer
B. ( (2x+y)(x+3y) )
Step 1
Concept
Split the middle term (7xy) as (6xy+xy). Exam tip: choose the pair with product (6) and sum (7).
Step 2
Why this answer is correct
The correct answer is B. ( (2x+y)(x+3y) ). Split the middle term (7xy) as (6xy+xy). Exam tip: choose the pair with product (6) and sum (7).
Step 3
Exam Tip
मध्य पद (7xy) को (6xy+xy) में तोड़ें। परीक्षा में ((2)(3)=6) और योग (7) वाली जोड़ी चुनें।
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\(6x^2-x-12\) का गुणनखंड रूप क्या होगा?
What will be the factorised form of \(6x^2-x-12\)?
#quadratic
#signs
#factorisation
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A ( (3x-4)(2x+3) )
B ( (6x-4)(x+3) )
C ( (3x+4)(2x-3) )
D ( (2x-4)(3x+3) )
Explanation opens after your attempt
Correct Answer
C. ( (3x+4)(2x-3) )
Step 1
Concept
Expanding gives ( (3x+4)(2x-3)=6x-2 -x-12 ). Exam tip: verify by expansion when signs are tricky.
Step 2
Why this answer is correct
The correct answer is C. ( (3x+4)(2x-3) ). Expanding gives ( (3x+4)(2x-3)=6x-2 -x-12 ). Exam tip: verify by expansion when signs are tricky.
Step 3
Exam Tip
फैलाने पर ( (3x+4)(2x-3)=6x-2 -x-12 ) मिलता है। परीक्षा में कठिन चिन्हों वाले प्रश्न में विस्तार से जांच करें।
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\(12a^2-7ab-b^2\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(12a^2-7ab-b^2\).
#quadratic in variables
#ac method
#factorisation
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A ( (3a+b)(4a-b) )
B ( (12a+b)(a-b) )
C ( (3a-b)(4a+b) )
D ( (4a- b)(3a+b) )
Explanation opens after your attempt
Correct Answer
D. ( (4a- b)(3a+b) )
Step 1
Concept
For (-7ab), write \(12a^2-8ab+ab-b^2\). Exam tip: when options look similar, confirm by expansion.
Step 2
Why this answer is correct
The correct answer is D. ( (4a- b)(3a+b) ). For (-7ab), write \(12a^2-8ab+ab-b^2\). Exam tip: when options look similar, confirm by expansion.
Step 3
Exam Tip
(-7ab) के लिए \(12a^2-8ab+ab-b^2\) बनता है। परीक्षा में विकल्प समान दिखें तो फैलाकर पुष्टि करें।
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\(x^4+5x^2+6\) को गुणनखंडों में बदलें।
Convert \(x^4+5x^2+6\) into factors.
#biquadratic
#factorisation
#substitution
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A ( \(x^2+1\)\(x^2+6\) )
B ( \(x^2+2\)\(x^2+3\) )
C ( (x+2)(x+3) )
D ( \(x^2-2\)\(x^2-3\) )
Explanation opens after your attempt
Correct Answer
B. ( \(x^2+2\)\(x^2+3\) )
Step 1
Concept
Treat \(x^2\) as a new term and factor like a quadratic. Exam tip: for \(x^4\) type questions, think \(u=x^2\).
Step 2
Why this answer is correct
The correct answer is B. ( \(x^2+2\)\(x^2+3\) ). Treat \(x^2\) as a new term and factor like a quadratic. Exam tip: for \(x^4\) type questions, think \(u=x^2\).
Step 3
Exam Tip
\(x^2\) को एक नया पद मानकर द्विघात की तरह गुणनखंड करें। परीक्षा में \(x^4\) वाले प्रश्न को \(u=x^2\) सोचकर हल करें।
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\(y^4-13y^2+36\) का सही गुणनखंड रूप क्या है?
What is the correct factorised form of \(y^4-13y^2+36\)?
#biquadratic
#middle term
#factorisation
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A ( \(y^2-4\)\(y^2-9\) )
B ( \(y^2+4\)\(y^2+9\) )
C ( (y-4)(y-9) )
D ( \(y^2-6\)\(y^2-6\) )
Explanation opens after your attempt
Correct Answer
A. ( \(y^2-4\)\(y^2-9\) )
Step 1
Concept
Taking \(y^2\) as one quantity, the product must be (36) and the sum (-13). Exam tip: identify the pair (-4) and (-9).
Step 2
Why this answer is correct
The correct answer is A. ( \(y^2-4\)\(y^2-9\) ). Taking \(y^2\) as one quantity, the product must be (36) and the sum (-13). Exam tip: identify the pair (-4) and (-9).
Step 3
Exam Tip
\(y^2\) को एक मात्रा मानने पर गुणनफल (36) और योग (-13) चाहिए। परीक्षा में (-4) और (-9) की जोड़ी पहचानें।
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\(x^2+4x-45\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2+4x-45\).
#quadratic
#sign choice
#factorisation
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A ( (x+9)(x-5) )
B ( (x-9)(x+5) )
C ( (x+15)(x-3) )
D ( (x-1)(x+45) )
Explanation opens after your attempt
Correct Answer
A. ( (x+9)(x-5) )
Step 1
Concept
The numbers (9) and (-5) have sum (4) and product (-45). Exam tip: with opposite signs, the larger magnitude gives the middle term sign.
Step 2
Why this answer is correct
The correct answer is A. ( (x+9)(x-5) ). The numbers (9) and (-5) have sum (4) and product (-45). Exam tip: with opposite signs, the larger magnitude gives the middle term sign.
Step 3
Exam Tip
(9) और (-5) का योग (4) और गुणनफल (-45) है। परीक्षा में अलग चिन्हों में बड़े परिमाण का चिन्ह मध्य पद देता है।
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\(3x^2-17x+10\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(3x^2-17x+10\)?
#quadratic
#ac method
#factorisation
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A ( (3x-10)(x-1) )
B ( (3x-2)(x-5) )
C ( (3x+2)(x+5) )
D ( (x-10)(3x-1) )
Explanation opens after your attempt
Correct Answer
B. ( (3x-2)(x-5) )
Step 1
Concept
Expanding gives ( (3x-2)(x-5)=3x-2 -17x+10 ). Exam tip: choose the pair with product (30) and sum (-17).
Step 2
Why this answer is correct
The correct answer is B. ( (3x-2)(x-5) ). Expanding gives ( (3x-2)(x-5)=3x-2 -17x+10 ). Exam tip: choose the pair with product (30) and sum (-17).
Step 3
Exam Tip
फैलाने पर ( (3x-2)(x-5)=3x-2 -17x+10 ) मिलता है। परीक्षा में (ac=30) और योग (-17) वाली जोड़ी लें।
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\(5u^2+13uv-6v^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(5u^2+13uv-6v^2\)?
#quadratic in variables
#middle term
#factorisation
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A ( (5u-2v)(u+3v) )
B ( (5u+2v)(u-3v) )
C ( (5u-2v)(u+3v) )
D ( (u+6v)(5u-v) )
Explanation opens after your attempt
Correct Answer
C. ( (5u-2v)(u+3v) )
Step 1
Concept
The split (15uv-2uv) gives the middle term (13uv). Exam tip: for a negative last term, check opposite signs.
Step 2
Why this answer is correct
The correct answer is C. ( (5u-2v)(u+3v) ). The split (15uv-2uv) gives the middle term (13uv). Exam tip: for a negative last term, check opposite signs.
Step 3
Exam Tip
(15uv-2uv) से मध्य पद (13uv) बनता है। परीक्षा में ऋणात्मक अंतिम पद के लिए विपरीत चिन्हों की जांच करें।
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\(7a^2-5ab-2b^2\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(7a^2-5ab-2b^2\).
#quadratic in variables
#verification
#factorisation
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A ( (7a+2b)(a-b) )
B ( (7a-b)(a+2b) )
C ( (7a-2b)(a+b) )
D ( (7a+2b)(a-b) )
Explanation opens after your attempt
Correct Answer
D. ( (7a+2b)(a-b) )
Step 1
Concept
Expanding gives \(7a^2-7ab+2ab-2b^2\). Exam tip: verify similar-looking options by expansion.
Step 2
Why this answer is correct
The correct answer is D. ( (7a+2b)(a-b) ). Expanding gives \(7a^2-7ab+2ab-2b^2\). Exam tip: verify similar-looking options by expansion.
Step 3
Exam Tip
फैलाने पर \(7a^2-7ab+2ab-2b^2\) मिलता है। परीक्षा में समान दिखने वाले विकल्पों को विस्तार से जांचें।
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\(x^4-10x^2+9\) का पूर्ण गुणनखंड रूप क्या है?
What is the complete factorised form of \(x^4-10x^2+9\)?
#biquadratic
#complete factorisation
#difference of squares
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A ( \(x^2-1\)\(x^2-9\) )
B ( \(x^2+1\)\(x^2+9\) )
C ( (x-1)(x+1)(x-3)(x+3) )
D ( \(x^2-3\)2 )
Explanation opens after your attempt
Correct Answer
C. ( (x-1)(x+1)(x-3)(x+3) )
Step 1
Concept
First we get (\(x^2-1\)\(x^2-9\)), and both are differences of squares. Exam tip: factor till the final complete form.
Step 2
Why this answer is correct
The correct answer is C. ( (x-1)(x+1)(x-3)(x+3) ). First we get (\(x^2-1\)\(x^2-9\)), and both are differences of squares. Exam tip: factor till the final complete form.
Step 3
Exam Tip
पहले (\(x^2-1\)\(x^2-9\)) मिलता है और दोनों अंतर वर्ग हैं। परीक्षा में पूर्ण गुणनखंड रूप के लिए अंतिम तक तोड़ें।
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\(x^2+7x+12-y^2\) का गुणनखंड रूप चुनिए।
Choose the factorised form of \(x^2+7x+12-y^2\).
#mixed factorisation
#verification
#quadratic
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A ( (x+3-y)(x+4+y) )
B ( (x+3+y)(x+4-y) )
C ( (x+3-y)(x+4+y) )
D ( (x+y+3)(x+y+4) )
Explanation opens after your attempt
Correct Answer
C. ( (x+3-y)(x+4+y) )
Step 1
Concept
Factoring \(x^2+7x+12\) as ((x+3)(x+4)) alone is not enough. Expanding the given option also gives the term \(-y^2\).
Step 2
Why this answer is correct
The correct answer is C. ( (x+3-y)(x+4+y) ). Factoring \(x^2+7x+12\) as ((x+3)(x+4)) alone is not enough. Expanding the given option also gives the term \(-y^2\).
Step 3
Exam Tip
\(x^2+7x+12\) को ((x+3)(x+4)) तोड़ना पर्याप्त नहीं है। दिए गए विकल्प को फैलाने पर सही पद \( -y^2 \) भी मिलता है।
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\(3x^2+2xy-8y^2\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(3x^2+2xy-8y^2\).
#quadratic in variables
#middle term
#factorisation
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A ( (3x-4y)(x+2y) )
B ( (3x+4y)(x-2y) )
C ( (3x-4y)(x+2y) )
D ( (x-4y)(3x+2y) )
Explanation opens after your attempt
Correct Answer
C. ( (3x-4y)(x+2y) )
Step 1
Concept
The split (6xy-4xy) gives (2xy). Exam tip: the signs are opposite because the last term is negative.
Step 2
Why this answer is correct
The correct answer is C. ( (3x-4y)(x+2y) ). The split (6xy-4xy) gives (2xy). Exam tip: the signs are opposite because the last term is negative.
Step 3
Exam Tip
(6xy-4xy) से (2xy) बनता है। परीक्षा में ऋणात्मक अंतिम पद के कारण चिन्ह विपरीत होंगे।
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\(10p^2-23pq+12q^2\) का गुणनखंड रूप क्या है?
What is the factorised form of \(10p^2-23pq+12q^2\)?
#quadratic in variables
#ac method
#factorisation
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A ( (5p-4q)(2p-3q) )
B ( (10p-3q)(p-4q) )
C ( (5p+4q)(2p+3q) )
D ( (5p-4q)(2p-3q) )
Explanation opens after your attempt
Correct Answer
D. ( (5p-4q)(2p-3q) )
Step 1
Concept
Expanding gives \(10p^2-15pq-8pq+12q^2\). Exam tip: check that (-15pq) and (-8pq) add to (-23pq).
Step 2
Why this answer is correct
The correct answer is D. ( (5p-4q)(2p-3q) ). Expanding gives \(10p^2-15pq-8pq+12q^2\). Exam tip: check that (-15pq) and (-8pq) add to (-23pq).
Step 3
Exam Tip
फैलाने पर \(10p^2-15pq-8pq+12q^2\) मिलता है। परीक्षा में (-15pq) और (-8pq) का योग (-23pq) जांचें।
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\(9x^4-30x^2+25\) का गुणनखंड रूप क्या है?
What is the factorised form of \(9x^4-30x^2+25\)?
#perfect square
#biquadratic
#factorisation
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A ( \(3x^2+5\)2 )
B ( \(9x^2-5\)2 )
C ( \(3x^2-5\)2 )
D ( (3x-5)(3x+5) )
Explanation opens after your attempt
Correct Answer
C. ( \(3x^2-5\)2 )
Step 1
Concept
It is (\(3x^2\)2 -2\cdot3x-2 \cdot5+52 ). Exam tip: identify perfect squares involving \(x^4\) too.
Step 2
Why this answer is correct
The correct answer is C. ( \(3x^2-5\)2 ). It is (\(3x^2\)2 -2\cdot3x-2 \cdot5+52 ). Exam tip: identify perfect squares involving \(x^4\) too.
Step 3
Exam Tip
यह (\(3x^2\)2 -2\cdot3x-2 \cdot5+52 ) है। परीक्षा में \(x^4\) वाले पूर्ण वर्ग को भी पहचानें।
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\(2x^2+5xy-12y^2\) का सही गुणनखंड कौन सा है?
Which is the correct factorisation of \(2x^2+5xy-12y^2\)?
#quadratic in variables
#ac method
#factorisation
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A ( (2x-3y)(x+4y) )
B ( (2x+3y)(x-4y) )
C ( (x+3y)(2x-4y) )
D ( (2x-3y)(x+4y) )
Explanation opens after your attempt
Correct Answer
D. ( (2x-3y)(x+4y) )
Step 1
Concept
The split (8xy-3xy) gives (5xy), and the product is \(-24x^2y^2\). Exam tip: split the middle term using the (ac) method.
Step 2
Why this answer is correct
The correct answer is D. ( (2x-3y)(x+4y) ). The split (8xy-3xy) gives (5xy), and the product is \(-24x^2y^2\). Exam tip: split the middle term using the (ac) method.
Step 3
Exam Tip
(8xy-3xy) से (5xy) बनता है और गुणनफल \(-24x^2y^2\) है। परीक्षा में (ac) विधि से मध्य पद तोड़ें।
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\(6x^2+11xy-10y^2\) का सही गुणनखंड चुनिए।
Choose the correct factorisation of \(6x^2+11xy-10y^2\).
#quadratic in variables
#signs
#factorisation
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A ( (3x-2y)(2x+5y) )
B ( (6x-5y)(x+2y) )
C ( (3x+2y)(2x-5y) )
D ( (3x-2y)(2x+5y) )
Explanation opens after your attempt
Correct Answer
D. ( (3x-2y)(2x+5y) )
Step 1
Concept
The split (15xy-4xy) gives (11xy). Exam tip: when the last term is negative, look for opposite signs.
Step 2
Why this answer is correct
The correct answer is D. ( (3x-2y)(2x+5y) ). The split (15xy-4xy) gives (11xy). Exam tip: when the last term is negative, look for opposite signs.
Step 3
Exam Tip
(15xy-4xy) से (11xy) बनता है। परीक्षा में अंतिम पद ऋणात्मक हो तो विपरीत चिन्हों की जोड़ी खोजें।
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