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quadratic factorisation MCQ Questions for Class 9

quadratic factorisation se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

Practice Questions

70 questions tagged with quadratic factorisation.

\(2x^2+5x-3\) का सही गुणनखंडन कौन सा है?

Which is the correct factorisation of \(2x^2+5x-3\)?

Explanation opens after your attempt
Correct Answer

A. ((2x-1)(x+3))

Step 1

Concept

((2x-1)(x+3)=2x-2+6x-x-3). This gives \(2x^2+5x-3\).

Step 2

Why this answer is correct

The correct answer is A. ((2x-1)(x+3)). ((2x-1)(x+3)=2x-2+6x-x-3). This gives \(2x^2+5x-3\).

Step 3

Exam Tip

((2x-1)(x+3)=2x-2+6x-x-3) है। इससे \(2x^2+5x-3\) मिलता है।

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\(3x^2+5x+2\) का गुणनखंडन चुनिए।

Choose the factorisation of \(3x^2+5x+2\).

Explanation opens after your attempt
Correct Answer

A. ((3x+2)(x+1))

Step 1

Concept

((3x+2)(x+1)=3x-2+3x+2x+2). The middle term (5x) is obtained.

Step 2

Why this answer is correct

The correct answer is A. ((3x+2)(x+1)). ((3x+2)(x+1)=3x-2+3x+2x+2). The middle term (5x) is obtained.

Step 3

Exam Tip

((3x+2)(x+1)=3x-2+3x+2x+2) है। मध्य पद (5x) मिलता है।

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\(x^2+3x-18\) का गुणनखंड रूप कौन सा है?

Which is the factor form of \(x^2+3x-18\)?

Explanation opens after your attempt
Correct Answer

D. ((x+6)(x-3))

Step 1

Concept

(6+(-3)=3) and (6\cdot(-3)=-18). Exam tip: match the sum of opposite signs.

Step 2

Why this answer is correct

The correct answer is D. ((x+6)(x-3)). (6+(-3)=3) and (6\cdot(-3)=-18). Exam tip: match the sum of opposite signs.

Step 3

Exam Tip

(6+(-3)=3) और (6\cdot(-3)=-18) है। परीक्षा में विपरीत चिह्नों का योग मिलाएं।

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\(x^2-9x+20\) का सही गुणनखंडन क्या होगा?

What will be the correct factorisation of \(x^2-9x+20\)?

Explanation opens after your attempt
Correct Answer

D. ((x-4)(x-5))

Step 1

Concept

(-4+(-5)=-9) and ((-4)(-5)=20). Therefore both factors are negative.

Step 2

Why this answer is correct

The correct answer is D. ((x-4)(x-5)). (-4+(-5)=-9) and ((-4)(-5)=20). Therefore both factors are negative.

Step 3

Exam Tip

(-4+(-5)=-9) और ((-4)(-5)=20) है। इसलिए दोनों कारक ऋण हैं।

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\(25x^2-1\) का गुणनखंडन कौन सा है?

Which is the factorisation of \(25x^2-1\)?

Explanation opens after your attempt
Correct Answer

C. ((5x-1)(5x+1))

Step 1

Concept

(25x-2=(5x)2) and \(1=1^2\). Difference of squares gives two factors.

Step 2

Why this answer is correct

The correct answer is C. ((5x-1)(5x+1)). (25x-2=(5x)2) and \(1=1^2\). Difference of squares gives two factors.

Step 3

Exam Tip

(25x-2=(5x)2) और \(1=1^2\) है। वर्गों के अंतर से दो गुणनखंड मिलते हैं।

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\(x^2-2x-15\) का सही गुणनखंड रूप कौन सा है?

Which is the correct factor form of \(x^2-2x-15\)?

Explanation opens after your attempt
Correct Answer

D. ((x-5)(x+3))

Step 1

Concept

(-5+3=-2) and \(-5\cdot3=-15\). So ((x-5)(x+3)) is correct.

Step 2

Why this answer is correct

The correct answer is D. ((x-5)(x+3)). (-5+3=-2) and \(-5\cdot3=-15\). So ((x-5)(x+3)) is correct.

Step 3

Exam Tip

(-5+3=-2) और \(-5\cdot3=-15\) है। इसलिए ((x-5)(x+3)) सही है।

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\(x^2+4x-21\) का गुणनखंडन क्या है?

What is the factorisation of \(x^2+4x-21\)?

Explanation opens after your attempt
Correct Answer

D. ((x+7)(x-3))

Step 1

Concept

(7+(-3)=4) and (7\cdot(-3)=-21). Exam tip: choose the larger factor with the correct sign.

Step 2

Why this answer is correct

The correct answer is D. ((x+7)(x-3)). (7+(-3)=4) and (7\cdot(-3)=-21). Exam tip: choose the larger factor with the correct sign.

Step 3

Exam Tip

(7+(-3)=4) और (7\cdot(-3)=-21) है। परीक्षा में बड़ा कारक सही चिह्न के साथ लें।

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\(6x^2+11x+3\) का सही गुणनखंडन चुनिए।

Choose the correct factorisation of \(6x^2+11x+3\).

Explanation opens after your attempt
Correct Answer

B. ((3x+1)(2x+3))

Step 1

Concept

((3x+1)(2x+3)=6x-2+9x+2x+3). Thus the middle term is (11x).

Step 2

Why this answer is correct

The correct answer is B. ((3x+1)(2x+3)). ((3x+1)(2x+3)=6x-2+9x+2x+3). Thus the middle term is (11x).

Step 3

Exam Tip

((3x+1)(2x+3)=6x-2+9x+2x+3) है। इसलिए मध्य पद (11x) बनता है।

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\(5x^2+13x+6\) का गुणनखंडन क्या होगा?

What will be the factorisation of \(5x^2+13x+6\)?

Explanation opens after your attempt
Correct Answer

D. ((5x+3)(x+2))

Step 1

Concept

((5x+3)(x+2)=5x-2+10x+3x+6). The middle term (13x) is obtained.

Step 2

Why this answer is correct

The correct answer is D. ((5x+3)(x+2)). ((5x+3)(x+2)=5x-2+10x+3x+6). The middle term (13x) is obtained.

Step 3

Exam Tip

((5x+3)(x+2)=5x-2+10x+3x+6) है। मध्य पद (13x) मिलता है।

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\(x^2-7x+10\) का सही गुणनखंड रूप क्या है?

What is the correct factor form of \(x^2-7x+10\)?

Explanation opens after your attempt
Correct Answer

B. ((x-5)(x-2))

Step 1

Concept

(-5+(-2)=-7) and ((-5)(-2)=10). Therefore both factors are negative.

Step 2

Why this answer is correct

The correct answer is B. ((x-5)(x-2)). (-5+(-2)=-7) and ((-5)(-2)=10). Therefore both factors are negative.

Step 3

Exam Tip

(-5+(-2)=-7) और ((-5)(-2)=10) है। इसलिए दोनों गुणनखंड ऋण होंगे।

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\(x^2+6x+5\) का गुणनखंडन कौन सा है?

Which is the factorisation of \(x^2+6x+5\)?

Explanation opens after your attempt
Correct Answer

D. ((x+1)(x+5))

Step 1

Concept

(1+5=6) and \(1\cdot5=5\). Exam tip: add the factors of the last term.

Step 2

Why this answer is correct

The correct answer is D. ((x+1)(x+5)). (1+5=6) and \(1\cdot5=5\). Exam tip: add the factors of the last term.

Step 3

Exam Tip

(1+5=6) और \(1\cdot5=5\) है। परीक्षा में अंतिम पद के कारक जोड़कर देखें।

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\(3x^2-x-2\) का गुणनखंडन चुनिए।

Choose the factorisation of \(3x^2-x-2\).

Explanation opens after your attempt
Correct Answer

D. ((3x+2)(x-1))

Step 1

Concept

((3x+2)(x-1)=3x-2-3x+2x-2). This gives \(3x^2-x-2\).

Step 2

Why this answer is correct

The correct answer is D. ((3x+2)(x-1)). ((3x+2)(x-1)=3x-2-3x+2x-2). This gives \(3x^2-x-2\).

Step 3

Exam Tip

((3x+2)(x-1)=3x-2-3x+2x-2) है। इससे \(3x^2-x-2\) मिलता है।

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\(2x^2-5x+3\) का सही गुणनखंडन क्या है?

What is the correct factorisation of \(2x^2-5x+3\)?

Explanation opens after your attempt
Correct Answer

C. ((2x-3)(x-1))

Step 1

Concept

((2x-3)(x-1)=2x-2-2x-3x+3). The middle term becomes (-5x).

Step 2

Why this answer is correct

The correct answer is C. ((2x-3)(x-1)). ((2x-3)(x-1)=2x-2-2x-3x+3). The middle term becomes (-5x).

Step 3

Exam Tip

((2x-3)(x-1)=2x-2-2x-3x+3) है। मध्य पद (-5x) बनता है।

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\(2x^2+7x+3\) का गुणनखंडन क्या है?

What is the factorisation of \(2x^2+7x+3\)?

Explanation opens after your attempt
Correct Answer

D. ((2x+1)(x+3))

Step 1

Concept

((2x+1)(x+3)=2x-2+6x+x+3). Thus the middle term is (7x).

Step 2

Why this answer is correct

The correct answer is D. ((2x+1)(x+3)). ((2x+1)(x+3)=2x-2+6x+x+3). Thus the middle term is (7x).

Step 3

Exam Tip

((2x+1)(x+3)=2x-2+6x+x+3) है। इसलिए मध्य पद (7x) बनता है।

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\(x^2+x-12\) का सही गुणनखंडन कौन सा है?

Which is the correct factorisation of \(x^2+x-12\)?

Explanation opens after your attempt
Correct Answer

D. ((x+4)(x-3))

Step 1

Concept

(4+(-3)=1) and (4\cdot(-3)=-12). Exam tip: check factors with opposite signs.

Step 2

Why this answer is correct

The correct answer is D. ((x+4)(x-3)). (4+(-3)=1) and (4\cdot(-3)=-12). Exam tip: check factors with opposite signs.

Step 3

Exam Tip

(4+(-3)=1) और (4\cdot(-3)=-12) है। परीक्षा में विपरीत चिह्न वाले कारक जांचें।

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\(x^2+9x+20\) के लिए ऐसे दो संख्याएं कौन सी हैं जिनका योग (9) और गुणन (20) है?

For \(x^2+9x+20\), which two numbers have sum (9) and product (20)?

Explanation opens after your attempt
Correct Answer

B. (4) और (5)(4) and (5)

Step 1

Concept

(4+5=9) and \(4\cdot5=20\). Exam tip: match both middle and constant terms.

Step 2

Why this answer is correct

The correct answer is B. (4) और (5) / (4) and (5). (4+5=9) and \(4\cdot5=20\). Exam tip: match both middle and constant terms.

Step 3

Exam Tip

(4+5=9) और \(4\cdot5=20\) है। परीक्षा में मध्य पद और स्थिर पद दोनों मिलाएं।

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\(14x^2-23x+6\) का सही गुणनखंड रूप चुनिए।

Choose the correct factorised form of \(14x^2-23x+6\).

Explanation opens after your attempt
Correct Answer

B. ((7x-2)(2x-3))

Step 1

Concept

((7x-2)(2x-3)) gives \(14x^2-21x-4x+6\). Exam tip: check that the middle term becomes (-23x), not (-25x).

Step 2

Why this answer is correct

The correct answer is B. ((7x-2)(2x-3)). ((7x-2)(2x-3)) gives \(14x^2-21x-4x+6\). Exam tip: check that the middle term becomes (-23x), not (-25x).

Step 3

Exam Tip

((7x-2)(2x-3)) से \(14x^2-21x-4x+6\) मिलता है। परीक्षा में (-25x) नहीं बल्कि (-23x) बनने की जांच करें।

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\(10x^2+31x+24\) के गुणनखंड कौन से हैं?

What are the factors of \(10x^2+31x+24\)?

Explanation opens after your attempt
Correct Answer

A. ((2x+3)(5x+8))

Step 1

Concept

((2x+3)(5x+8)) gives \(10x^2+16x+15x+24\). Exam tip: add both parts of the middle term.

Step 2

Why this answer is correct

The correct answer is A. ((2x+3)(5x+8)). ((2x+3)(5x+8)) gives \(10x^2+16x+15x+24\). Exam tip: add both parts of the middle term.

Step 3

Exam Tip

((2x+3)(5x+8)) से \(10x^2+16x+15x+24\) मिलता है। परीक्षा में मध्य पद के दोनों हिस्से जोड़कर देखें।

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\(5m^2-13mn-6n^2\) का सही गुणनखंड रूप कौन सा है?

Which is the correct factorised form of \(5m^2-13mn-6n^2\)?

Explanation opens after your attempt
Correct Answer

A. ((5m+2n)(m-3n))

Step 1

Concept

((5m+2n)(m-3n)) gives \(5m^2-15mn+2mn-6n^2\). Exam tip: use opposite signs for a negative constant term.

Step 2

Why this answer is correct

The correct answer is A. ((5m+2n)(m-3n)). ((5m+2n)(m-3n)) gives \(5m^2-15mn+2mn-6n^2\). Exam tip: use opposite signs for a negative constant term.

Step 3

Exam Tip

((5m+2n)(m-3n)) से \(5m^2-15mn+2mn-6n^2\) मिलता है। परीक्षा में ऋण स्थिर पद के लिए विपरीत चिह्न रखें।

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\(18x^2-21x-10\) को गुणनखंडित कीजिए।

Factorise \(18x^2-21x-10\).

Explanation opens after your attempt
Correct Answer

B. ((6x-5)(3x+2))

Step 1

Concept

((6x-5)(3x+2)) gives \(18x^2+12x-15x-10\). Exam tip: confirm that the middle term becomes (-21x).

Step 2

Why this answer is correct

The correct answer is B. ((6x-5)(3x+2)). ((6x-5)(3x+2)) gives \(18x^2+12x-15x-10\). Exam tip: confirm that the middle term becomes (-21x).

Step 3

Exam Tip

((6x-5)(3x+2)) से \(18x^2+12x-15x-10\) मिलता है। परीक्षा में मध्य पद (-21x) बनने की पुष्टि करें।

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\(15x^2+22x+8\) का सही गुणनखंड रूप कौन सा है?

Which is the correct factorised form of \(15x^2+22x+8\)?

Explanation opens after your attempt
Correct Answer

A. ((3x+2)(5x+4))

Step 1

Concept

((3x+2)(5x+4)) gives \(15x^2+12x+10x+8\). Exam tip: check options by expansion.

Step 2

Why this answer is correct

The correct answer is A. ((3x+2)(5x+4)). ((3x+2)(5x+4)) gives \(15x^2+12x+10x+8\). Exam tip: check options by expansion.

Step 3

Exam Tip

((3x+2)(5x+4)) से \(15x^2+12x+10x+8\) मिलता है। परीक्षा में विकल्पों को फैलाकर जांचें।

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\(x^2+2x-63\) के गुणनखंड कौन से हैं?

What are the factors of \(x^2+2x-63\)?

Explanation opens after your attempt
Correct Answer

A. ((x+9)(x-7))

Step 1

Concept

Since (9-7=2) and (9\cdot(-7)=-63). Exam tip: use opposite signs for a negative constant term.

Step 2

Why this answer is correct

The correct answer is A. ((x+9)(x-7)). Since (9-7=2) and (9\cdot(-7)=-63). Exam tip: use opposite signs for a negative constant term.

Step 3

Exam Tip

(9-7=2) और (9\cdot(-7)=-63) है। परीक्षा में ऋण स्थिर पद के लिए विपरीत चिह्न लें।

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\(3x^2-14x+8\) के गुणनखंड कौन से हैं?

What are the factors of \(3x^2-14x+8\)?

Explanation opens after your attempt
Correct Answer

A. ((3x-2)(x-4))

Step 1

Concept

The terms (-12x) and (-2x) combine to (-14x). Exam tip: group after splitting the middle term.

Step 2

Why this answer is correct

The correct answer is A. ((3x-2)(x-4)). The terms (-12x) and (-2x) combine to (-14x). Exam tip: group after splitting the middle term.

Step 3

Exam Tip

(-12x) और (-2x) मिलकर (-14x) देते हैं। परीक्षा में मध्य पद विभाजन के बाद समूह बनाएं।

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\(2x^2+9x+10\) को गुणनखंडित करने पर कौन सा उत्तर सही है?

Which answer is correct after factorising \(2x^2+9x+10\)?

Explanation opens after your attempt
Correct Answer

A. ((2x+5)(x+2))

Step 1

Concept

Expanding gives \(2x^2+4x+5x+10=2x^2+9x+10\). Exam tip: verify the answer by multiplication.

Step 2

Why this answer is correct

The correct answer is A. ((2x+5)(x+2)). Expanding gives \(2x^2+4x+5x+10=2x^2+9x+10\). Exam tip: verify the answer by multiplication.

Step 3

Exam Tip

विस्तार से \(2x^2+4x+5x+10=2x^2+9x+10\) मिलता है। परीक्षा में गुणा करके उत्तर सत्यापित करें।

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\(6x^2+11x+3\) का सही गुणनखंड रूप कौन सा है?

Which is the correct factorised form of \(6x^2+11x+3\)?

Explanation opens after your attempt
Correct Answer

A. ((3x+1)(2x+3))

Step 1

Concept

Expanding gives \(6x^2+9x+2x+3=6x^2+11x+3\). Exam tip: verify the split of the middle term.

Step 2

Why this answer is correct

The correct answer is A. ((3x+1)(2x+3)). Expanding gives \(6x^2+9x+2x+3=6x^2+11x+3\). Exam tip: verify the split of the middle term.

Step 3

Exam Tip

विस्तार करने पर \(6x^2+9x+2x+3=6x^2+11x+3\) मिलता है। परीक्षा में मध्य पद विभाजन जांचें।

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\(x^2-2x-35\) के गुणनखंड कौन से हैं?

What are the factors of \(x^2-2x-35\)?

Explanation opens after your attempt
Correct Answer

A. ((x-7)(x+5))

Step 1

Concept

Since (-7+5=-2) and ((-7)(5)=-35). Exam tip: choose factors with opposite signs carefully.

Step 2

Why this answer is correct

The correct answer is A. ((x-7)(x+5)). Since (-7+5=-2) and ((-7)(5)=-35). Exam tip: choose factors with opposite signs carefully.

Step 3

Exam Tip

(-7+5=-2) और ((-7)(5)=-35) है। परीक्षा में विपरीत चिह्न वाले गुणनखंड सावधानी से चुनें।

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\(y^2-11y+30\) को गुणनखंडित करने पर क्या मिलेगा?

What do we get by factorising \(y^2-11y+30\)?

Explanation opens after your attempt
Correct Answer

A. ((y-5)(y-6))

Step 1

Concept

Here (-5-6=-11) and ((-5)(-6)=30). Exam tip: for a negative middle term, both factors may be negative.

Step 2

Why this answer is correct

The correct answer is A. ((y-5)(y-6)). Here (-5-6=-11) and ((-5)(-6)=30). Exam tip: for a negative middle term, both factors may be negative.

Step 3

Exam Tip

(-5-6=-11) और ((-5)(-6)=30) है। परीक्षा में ऋण मध्य पद के लिए दोनों कारक ऋण हो सकते हैं।

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\(x^2+7x+12\) के सही गुणनखंड कौन से हैं?

Which are the correct factors of \(x^2+7x+12\)?

Explanation opens after your attempt
Correct Answer

B. ((x+3)(x+4))

Step 1

Concept

Since (3+4=7) and \(3\cdot4=12\), the correct factors are ((x+3)(x+4)). Exam tip: match both sum and product.

Step 2

Why this answer is correct

The correct answer is B. ((x+3)(x+4)). Since (3+4=7) and \(3\cdot4=12\), the correct factors are ((x+3)(x+4)). Exam tip: match both sum and product.

Step 3

Exam Tip

(3+4=7) और \(3\cdot4=12\) है इसलिए सही गुणनखंड ((x+3)(x+4)) हैं। परीक्षा में योग और गुणनफल दोनों मिलाएं।

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\(10a^2+11a-6\) को गुणनखंडित कीजिए।

Factorise \(10a^2+11a-6\).

Explanation opens after your attempt
Correct Answer

A. ((5a-2)(2a+3))

Step 1

Concept

((5a-2)(2a+3)) gives \(10a^2+15a-4a-6\). In exams, confirm the middle term (11a).

Step 2

Why this answer is correct

The correct answer is A. ((5a-2)(2a+3)). ((5a-2)(2a+3)) gives \(10a^2+15a-4a-6\). In exams, confirm the middle term (11a).

Step 3

Exam Tip

((5a-2)(2a+3)) से \(10a^2+15a-4a-6\) मिलता है। परीक्षा में मध्य पद (11a) की पुष्टि करें।

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\(7x^2+29x+30\) का गुणनखंड रूप क्या है?

What is the factorised form of \(7x^2+29x+30\)?

Explanation opens after your attempt
Correct Answer

A. ((7x+15)(x+2))

Step 1

Concept

((7x+15)(x+2)) gives \(7x^2+14x+15x+30\). In exams, check that the middle terms add to (29x).

Step 2

Why this answer is correct

The correct answer is A. ((7x+15)(x+2)). ((7x+15)(x+2)) gives \(7x^2+14x+15x+30\). In exams, check that the middle terms add to (29x).

Step 3

Exam Tip

((7x+15)(x+2)) से \(7x^2+14x+15x+30\) मिलता है। परीक्षा में मध्य पदों का योग (29x) जाँचें।

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