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cubic factorisation MCQ Questions for Class 9

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4 questions tagged with cubic factorisation.

Question 1/4 Expert Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 71

\(x^3+y^3+x^2y+xy^2\) का गुणनखंड रूप क्या है?

What is the factorised form of \(x^3+y^3+x^2y+xy^2\)?

Explanation opens after your attempt
Correct Answer

B. ((x+y)\(x^2+xy+y^2\))

Step 1

Concept

Grouping all terms gives a common factor like (x-2(x+y)+y-2(x+y)+xy(x+y)). Exam tip: take ((x+y)) common and add the remaining terms.

Step 2

Why this answer is correct

The correct answer is B. ((x+y)\(x^2+xy+y^2\)). Grouping all terms gives a common factor like (x-2(x+y)+y-2(x+y)+xy(x+y)). Exam tip: take ((x+y)) common and add the remaining terms.

Step 3

Exam Tip

सभी पदों को समूहित करने पर (x-2(x+y)+y-2(x+y)+xy(x+y)) जैसा समान गुणनखंड बनता है। परीक्षा में ((x+y)) सामान्य लेकर शेष पद जोड़ें।

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Question 2/4 Expert Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 71

\(64a^3-125b^3\) का सही गुणनखंड रूप चुनिए।

Choose the correct factorised form of \(64a^3-125b^3\).

Explanation opens after your attempt
Correct Answer

A. ((4a-5b)\(16a^2+20ab+25b^2\))

Step 1

Concept

Here (64a-3=(4a)3) and (125b-3=(5b)3). Exam tip: in the difference formula, the second bracket has positive (20ab).

Step 2

Why this answer is correct

The correct answer is A. ((4a-5b)\(16a^2+20ab+25b^2\)). Here (64a-3=(4a)3) and (125b-3=(5b)3). Exam tip: in the difference formula, the second bracket has positive (20ab).

Step 3

Exam Tip

(64a-3=(4a)3) और (125b-3=(5b)3) हैं। परीक्षा में अंतर के सूत्र में दूसरे कोष्ठक में धन (20ab) आएगा।

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Question 3/4 Expert Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 71

\(x^3+8\) को गुणनखंडित करने पर क्या मिलेगा?

What do we get by factorising \(x^3+8\)?

Explanation opens after your attempt
Correct Answer

A. ((x+2)\(x^2-2x+4\))

Step 1

Concept

This is \(x^3+2^3\), so use the sum of cubes formula. Exam tip: keep the middle term negative in the second bracket.

Step 2

Why this answer is correct

The correct answer is A. ((x+2)\(x^2-2x+4\)). This is \(x^3+2^3\), so use the sum of cubes formula. Exam tip: keep the middle term negative in the second bracket.

Step 3

Exam Tip

यह \(x^3+2^3\) है इसलिए घनों के योग का सूत्र लगेगा। परीक्षा में दूसरे कोष्ठक में बीच का पद ऋण रखें।

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Question 4/4 Hard Mathematics Exploring Algebraic Identities Factorisation Class 9 Level 69

\(x^3-9x\) का पूर्ण गुणनखंडन क्या है?

What is the complete factorisation of \(x^3-9x\)?

Explanation opens after your attempt
Correct Answer

C. (x(x-3)(x+3))

Step 1

Concept

First take (x) common to get (x\(x^2-9\)). Then factor (x-2-9=(x-3)(x+3)).

Step 2

Why this answer is correct

The correct answer is C. (x(x-3)(x+3)). First take (x) common to get (x\(x^2-9\)). Then factor (x-2-9=(x-3)(x+3)).

Step 3

Exam Tip

पहले (x) समान निकालकर (x\(x^2-9\)) मिलता है। फिर (x-2-9=(x-3)(x+3)) करें।

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