Concept-wise Practice

factor form MCQ Questions for Class 10

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

Practice Questions

28 questions tagged with factor form.

(x-2-(a+b)x+ab=0) की जड़ें कौन-सी हैं?

What are the roots of (x-2-(a+b)x+ab=0)?

Explanation opens after your attempt
Correct Answer

A. (a) और (b)(a) and (b)

Step 1

Concept

The equation can be written as ((x-a)(x-b)=0). Therefore the roots are (a) and (b).

Step 2

Why this answer is correct

The correct answer is A. (a) और (b) / (a) and (b). The equation can be written as ((x-a)(x-b)=0). Therefore the roots are (a) and (b).

Step 3

Exam Tip

समीकरण ((x-a)(x-b)=0) के रूप में लिखा जा सकता है। इसलिए जड़ें (a) और (b) हैं।

Open Question Page
Ask Friends

यदि ((x-4)(x+9)=0) है तो मूल कौन से होंगे?

If ((x-4)(x+9)=0), what are the roots?

Explanation opens after your attempt
Correct Answer

C. (4) और (-9)(4) and (-9)

Step 1

Concept

By the zero product rule, (x-4=0) or (x+9=0). Therefore the roots are (4) and (-9).

Step 2

Why this answer is correct

The correct answer is C. (4) और (-9) / (4) and (-9). By the zero product rule, (x-4=0) or (x+9=0). Therefore the roots are (4) and (-9).

Step 3

Exam Tip

शून्य गुणनफल नियम से (x-4=0) या (x+9=0) होगा। इसलिए मूल (4) और (-9) हैं।

Open Question Page
Ask Friends

यदि ((x+1)(x-8)=0) है तो मूल कौन से होंगे?

If ((x+1)(x-8)=0), what are the roots?

Explanation opens after your attempt
Correct Answer

B. (-1) और (8)(-1) and (8)

Step 1

Concept

By the zero product rule, (x+1=0) or (x-8=0). Therefore the roots are (-1) and (8).

Step 2

Why this answer is correct

The correct answer is B. (-1) और (8) / (-1) and (8). By the zero product rule, (x+1=0) or (x-8=0). Therefore the roots are (-1) and (8).

Step 3

Exam Tip

शून्य गुणनफल नियम से (x+1=0) या (x-8=0) होगा। इसलिए मूल (-1) और (8) हैं।

Open Question Page
Ask Friends

यदि ((x-2)(x+7)=0) है तो मूल कौन से होंगे?

If ((x-2)(x+7)=0) then what are the roots?

Explanation opens after your attempt
Correct Answer

C. (2) और (-7)(2) and (-7)

Step 1

Concept

By the zero product rule (x-2=0) or (x+7=0). Hence the roots are (2) and (-7).

Step 2

Why this answer is correct

The correct answer is C. (2) और (-7) / (2) and (-7). By the zero product rule (x-2=0) or (x+7=0). Hence the roots are (2) and (-7).

Step 3

Exam Tip

शून्य गुणनफल नियम से (x-2=0) या (x+7=0) होगा। इसलिए मूल (2) और (-7) हैं।

Open Question Page
Ask Friends

समीकरण \(x^2+11x+30=0\) को गुणनखंड रूप में कौन-सा लिखा जा सकता है?

Which factor form can represent \(x^2+11x+30=0\)?

Explanation opens after your attempt
Correct Answer

A. ((x+5)(x+6)=0)

Step 1

Concept

\(5\cdot6=30\) and (5+6=11). Therefore the correct factors are ((x+5)(x+6)).

Step 2

Why this answer is correct

The correct answer is A. ((x+5)(x+6)=0). \(5\cdot6=30\) and (5+6=11). Therefore the correct factors are ((x+5)(x+6)).

Step 3

Exam Tip

\(5\cdot6=30\) और (5+6=11) है। इसलिए सही गुणनखंड ((x+5)(x+6)) हैं।

Open Question Page
Ask Friends

समीकरण \(x^2+9x+20=0\) को गुणनखंड रूप में कौन-सा लिखा जा सकता है?

Which factor form can represent \(x^2+9x+20=0\)?

Explanation opens after your attempt
Correct Answer

A. ((x+4)(x+5)=0)

Step 1

Concept

\(4\cdot5=20\) and (4+5=9). Therefore the correct factors are ((x+4)(x+5)).

Step 2

Why this answer is correct

The correct answer is A. ((x+4)(x+5)=0). \(4\cdot5=20\) and (4+5=9). Therefore the correct factors are ((x+4)(x+5)).

Step 3

Exam Tip

\(4\cdot5=20\) और (4+5=9) है। इसलिए सही गुणनखंड ((x+4)(x+5)) हैं।

Open Question Page
Ask Friends

समीकरण \(x^2+7x+12=0\) को गुणनखंड रूप में कौन-सा लिखा जा सकता है?

Which factor form can represent \(x^2+7x+12=0\)?

Explanation opens after your attempt
Correct Answer

A. ((x+3)(x+4)=0)

Step 1

Concept

The product of (3) and (4) is (12), and their sum is (7). Therefore ((x+3)(x+4)=0) is correct.

Step 2

Why this answer is correct

The correct answer is A. ((x+3)(x+4)=0). The product of (3) and (4) is (12), and their sum is (7). Therefore ((x+3)(x+4)=0) is correct.

Step 3

Exam Tip

(3) और (4) का गुणनफल (12) और योग (7) है। इसलिए ((x+3)(x+4)=0) सही है।

Open Question Page
Ask Friends

कौन सा विकल्प \(x^2+x-12=0\) का गुणनखंड रूप है?

Which option is the factor form of \(x^2+x-12=0\)?

Explanation opens after your attempt
Correct Answer

A. ((x+4)(x-3)=0)

Step 1

Concept

Expanding ((x+4)(x-3)) gives \(x^2+x-12\). To check factors, expand them.

Step 2

Why this answer is correct

The correct answer is A. ((x+4)(x-3)=0). Expanding ((x+4)(x-3)) gives \(x^2+x-12\). To check factors, expand them.

Step 3

Exam Tip

((x+4)(x-3)) फैलाने पर \(x^2+x-12\) मिलता है। गुणनखंड जांचने के लिए विस्तार करें।

Open Question Page
Ask Friends

\(x^2-49=0\) को गुणनखंड रूप में कैसे लिखेंगे?

How do we write \(x^2-49=0\) in factor form?

Explanation opens after your attempt
Correct Answer

A. ((x-7)(x+7)=0)

Step 1

Concept

\(x^2-49\) is a difference of squares. Hence it becomes ((x-7)(x+7)).

Step 2

Why this answer is correct

The correct answer is A. ((x-7)(x+7)=0). \(x^2-49\) is a difference of squares. Hence it becomes ((x-7)(x+7)).

Step 3

Exam Tip

\(x^2-49\) वर्गों का अंतर है। इसलिए यह ((x-7)(x+7)) बनता है।

Open Question Page
Ask Friends

कौन सा विकल्प \(x^2+10x+25=0\) को गुणनखंड रूप में दिखाता है?

Which option shows \(x^2+10x+25=0\) in factor form?

Explanation opens after your attempt
Correct Answer

A. ((x+5)2=0)

Step 1

Concept

\(x^2+10x+25\) is a perfect square. It equals ((x+5)2).

Step 2

Why this answer is correct

The correct answer is A. ((x+5)2=0). \(x^2+10x+25\) is a perfect square. It equals ((x+5)2).

Step 3

Exam Tip

\(x^2+10x+25\) पूर्ण वर्ग है। यह ((x+5)2) के बराबर है।

Open Question Page
Ask Friends

कौन सा विकल्प \(x^2-2x-15=0\) का गुणनखंड रूप है?

Which option is the factor form of \(x^2-2x-15=0\)?

Explanation opens after your attempt
Correct Answer

A. \((x-5)(x+3)=0\)

Step 1

Concept

Expanding ((x-5)(x+3)) gives \(x^2-2x-15\). To check factors, expand them.

Step 2

Why this answer is correct

The correct answer is A. \((x-5)(x+3)=0\). Expanding ((x-5)(x+3)) gives \(x^2-2x-15\). To check factors, expand them.

Step 3

Exam Tip

((x-5)(x+3)) फैलाने पर \(x^2-2x-15\) मिलता है। गुणनखंड जांचने के लिए विस्तार करें।

Open Question Page
Ask Friends

\(x^2-16=0\) को गुणनखंड रूप में कैसे लिखेंगे?

How do we write \(x^2-16=0\) in factor form?

Explanation opens after your attempt
Correct Answer

A. \((x-4)(x+4)=0\)

Step 1

Concept

\(x^2-16\) is a difference of squares. Hence it becomes ((x-4)(x+4)).

Step 2

Why this answer is correct

The correct answer is A. \((x-4)(x+4)=0\). \(x^2-16\) is a difference of squares. Hence it becomes ((x-4)(x+4)).

Step 3

Exam Tip

\(x^2-16\) वर्गों का अंतर है। इसलिए यह ((x-4)(x+4)) बनता है।

Open Question Page
Ask Friends

कौन सा विकल्प \(x^2+6x+9=0\) को गुणनखंड रूप में दिखाता है?

Which option shows \(x^2+6x+9=0\) in factor form?

Explanation opens after your attempt
Correct Answer

A. \((x+3)^2=0\)

Step 1

Concept

\(x^2+6x+9\) is a perfect square. It equals ((x+3)2).

Step 2

Why this answer is correct

The correct answer is A. \((x+3)^2=0\). \(x^2+6x+9\) is a perfect square. It equals ((x+3)2).

Step 3

Exam Tip

\(x^2+6x+9\) एक पूर्ण वर्ग है। यह ((x+3)2) के बराबर है।

Open Question Page
Ask Friends

यदि बहुपद (p(x)=5(x+1)(x-2)(x-4)) है तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?

If (p(x)=5(x+1)(x-2)(x-4)), at how many distinct points will the graph cut the (x)-axis?

Explanation opens after your attempt
Correct Answer

A. तीनThree

Step 1

Concept

The factors give zeroes (-1), (2), and (4). Three distinct zeroes give three distinct (x)-intercepts.

Step 2

Why this answer is correct

The correct answer is A. तीन / Three. The factors give zeroes (-1), (2), and (4). Three distinct zeroes give three distinct (x)-intercepts.

Step 3

Exam Tip

गुणनखंडों से शून्यक (-1), (2), और (4) हैं। तीन अलग शून्यक तीन अलग (x)-प्रतिच्छेद देते हैं।

Open Question Page
Ask Friends

यदि किसी द्विघात का ग्राफ (x)-अक्ष को ((m,0)) और ((n,0)) पर काटता है तो कौन सा बहुपद उन्हीं शून्यकों वाला हो सकता है?

If a quadratic graph cuts the (x)-axis at ((m,0)) and ((n,0)), which polynomial can have the same zeroes?

Explanation opens after your attempt
Correct Answer

A. (k(x-m)(x-n)), जहाँ \(k\neq0\)(k(x-m)(x-n)), where \(k\neq0\)

Step 1

Concept

For zeroes (m) and (n), the factors are ((x-m)) and ((x-n)). A non-zero multiplier does not change zeroes.

Step 2

Why this answer is correct

The correct answer is A. (k(x-m)(x-n)), जहाँ \(k\neq0\) / (k(x-m)(x-n)), where \(k\neq0\). For zeroes (m) and (n), the factors are ((x-m)) and ((x-n)). A non-zero multiplier does not change zeroes.

Step 3

Exam Tip

शून्यक (m) और (n) के लिए गुणनखंड ((x-m)) और ((x-n)) होते हैं। गैर शून्य गुणक शून्यक नहीं बदलता।

Open Question Page
Ask Friends

यदि (p(x)=-(x-3)(x+1)) है तो ग्राफ के शून्यक कौन से हैं?

If (p(x)=-(x-3)(x+1)), what are the zeroes of the graph?

Explanation opens after your attempt
Correct Answer

A. (3) और (-1)(3) and (-1)

Step 1

Concept

The outside negative sign does not change the zeroes. Set the factors equal to zero.

Step 2

Why this answer is correct

The correct answer is A. (3) और (-1) / (3) and (-1). The outside negative sign does not change the zeroes. Set the factors equal to zero.

Step 3

Exam Tip

बाहर का ऋण चिह्न शून्यकों को नहीं बदलता। गुणनखंडों को शून्य रखकर उत्तर निकालें।

Open Question Page
Ask Friends

यदि बहुपद (p(x)=2(x-1)(x+4)) है तो ग्राफ के (x)-प्रतिच्छेद कौन से हैं?

If (p(x)=2(x-1)(x+4)), what are the (x)-intercepts of its graph?

Explanation opens after your attempt
Correct Answer

A. ((1,0)) और ((-4,0))((1,0)) and ((-4,0))

Step 1

Concept

Making the factors zero gives (x=1) and (x=-4). Write (x)-intercepts as ((x,0)).

Step 2

Why this answer is correct

The correct answer is A. ((1,0)) और ((-4,0)) / ((1,0)) and ((-4,0)). Making the factors zero gives (x=1) and (x=-4). Write (x)-intercepts as ((x,0)).

Step 3

Exam Tip

गुणनखंड शून्य करने पर (x=1) और (x=-4) मिलते हैं। (x)-प्रतिच्छेद को ((x,0)) रूप में लिखें।

Open Question Page
Ask Friends

यदि (p(x)=-(x-11)(x+13)) है, तो (x<-13) के लिए ग्राफ (x)-अक्ष के किस ओर होगा?

If (p(x)=-(x-11)(x+13)), on which side of the (x)-axis will the graph lie for (x<-13)?

Explanation opens after your attempt
Correct Answer

B. नीचेBelow

Step 1

Concept

For (x<-13), both factors are negative and the outside negative makes the value negative. Tip: check factor signs first.

Step 2

Why this answer is correct

The correct answer is B. नीचे / Below. For (x<-13), both factors are negative and the outside negative makes the value negative. Tip: check factor signs first.

Step 3

Exam Tip

(x<-13) पर दोनों कारक ऋणात्मक हैं और बाहर का ऋण चिन्ह मान को ऋणात्मक बनाता है। टिप: पहले कारकों का चिह्न देखें।

Open Question Page
Ask Friends

यदि (p(x)=(x+9)(x-5)(x-12)) है, तो (5<x<12) में (p(x)) का चिह्न क्या होगा?

If (p(x)=(x+9)(x-5)(x-12)), what will be the sign of (p(x)) for (5<x<12)?

Explanation opens after your attempt
Correct Answer

B. ऋणात्मकNegative

Step 1

Concept

In this interval the first two factors are positive and the third is negative, so the product is negative. Tip: check the sign of each factor separately.

Step 2

Why this answer is correct

The correct answer is B. ऋणात्मक / Negative. In this interval the first two factors are positive and the third is negative, so the product is negative. Tip: check the sign of each factor separately.

Step 3

Exam Tip

इस अंतराल में पहले दो कारक धनात्मक और तीसरा ऋणात्मक है, इसलिए गुणनफल ऋणात्मक है। टिप: प्रत्येक कारक का चिह्न अलग जांचें।

Open Question Page
Ask Friends

यदि (p(x)=-(x-9)(x+11)) है, तो (x<-11) के लिए ग्राफ (x)-अक्ष के किस ओर होगा?

If (p(x)=-(x-9)(x+11)), on which side of the (x)-axis will the graph lie for (x<-11)?

Explanation opens after your attempt
Correct Answer

B. नीचेBelow

Step 1

Concept

For (x<-11), both factors are negative and the outside negative makes the value negative. Tip: check factor signs first.

Step 2

Why this answer is correct

The correct answer is B. नीचे / Below. For (x<-11), both factors are negative and the outside negative makes the value negative. Tip: check factor signs first.

Step 3

Exam Tip

(x<-11) पर दोनों कारक ऋणात्मक हैं और बाहर का ऋण चिन्ह मान को ऋणात्मक बनाता है। टिप: पहले कारकों का चिह्न देखें।

Open Question Page
Ask Friends

यदि (p(x)=(x+6)(x-4)(x-10)) है, तो (4<x<10) में (p(x)) का चिह्न क्या होगा?

If (p(x)=(x+6)(x-4)(x-10)), what will be the sign of (p(x)) for (4<x<10)?

Explanation opens after your attempt
Correct Answer

B. ऋणात्मकNegative

Step 1

Concept

In this interval the first two factors are positive and the third is negative, so the product is negative. Tip: check the sign of each factor separately.

Step 2

Why this answer is correct

The correct answer is B. ऋणात्मक / Negative. In this interval the first two factors are positive and the third is negative, so the product is negative. Tip: check the sign of each factor separately.

Step 3

Exam Tip

इस अंतराल में पहले दो कारक धनात्मक और तीसरा ऋणात्मक है, इसलिए गुणनफल ऋणात्मक है। टिप: प्रत्येक कारक का चिह्न अलग जांचें।

Open Question Page
Ask Friends

यदि (p(x)=-(x-7)(x+9)) है तो (x<-9) के लिए ग्राफ (x)-अक्ष के किस ओर होगा?

If (p(x)=-(x-7)(x+9)), on which side of the (x)-axis will the graph lie for (x<-9)?

Explanation opens after your attempt
Correct Answer

B. नीचेBelow

Step 1

Concept

For (x<-9), both factors are negative and the outside negative makes the value negative. Tip: check factor signs first.

Step 2

Why this answer is correct

The correct answer is B. नीचे / Below. For (x<-9), both factors are negative and the outside negative makes the value negative. Tip: check factor signs first.

Step 3

Exam Tip

(x<-9) पर दोनों कारक ऋणात्मक हैं और बाहर का ऋण चिन्ह मान को ऋणात्मक बनाता है। टिप: पहले कारकों का चिह्न देखें।

Open Question Page
Ask Friends

यदि (p(x)=(x+5)(x-3)(x-9)) है तो (3<x<9) में (p(x)) का चिह्न क्या होगा?

If (p(x)=(x+5)(x-3)(x-9)), what will be the sign of (p(x)) for (3<x<9)?

Explanation opens after your attempt
Correct Answer

B. ऋणात्मकNegative

Step 1

Concept

In this interval the first two factors are positive and the third is negative, so the product is negative. Tip: check factor signs separately.

Step 2

Why this answer is correct

The correct answer is B. ऋणात्मक / Negative. In this interval the first two factors are positive and the third is negative, so the product is negative. Tip: check factor signs separately.

Step 3

Exam Tip

इस अंतराल में पहले दो कारक धनात्मक और तीसरा ऋणात्मक है इसलिए गुणनफल ऋणात्मक है। टिप: कारकों के चिह्न अलग-अलग जांचें।

Open Question Page
Ask Friends

यदि (p(x)=-(x-4)(x+8)) है, तो (x<-8) के लिए ग्राफ (x)-अक्ष के किस ओर होगा?

If (p(x)=-(x-4)(x+8)), on which side of the (x)-axis will the graph lie for (x<-8)?

Explanation opens after your attempt
Correct Answer

B. नीचेBelow

Step 1

Concept

For (x<-8), both factors are negative and the outside negative makes the value negative. Tip: check factor signs first.

Step 2

Why this answer is correct

The correct answer is B. नीचे / Below. For (x<-8), both factors are negative and the outside negative makes the value negative. Tip: check factor signs first.

Step 3

Exam Tip

(x<-8) पर दोनों कारक ऋणात्मक हैं और बाहर का ऋण चिन्ह मान को ऋणात्मक बनाता है। टिप: पहले कारकों का चिह्न देखें।

Open Question Page
Ask Friends

यदि (p(x)=(x+4)(x-2)(x-7)) है, तो (2<x<7) में (p(x)) का चिह्न क्या होगा?

If (p(x)=(x+4)(x-2)(x-7)), what will be the sign of (p(x)) for (2<x<7)?

Explanation opens after your attempt
Correct Answer

B. ऋणात्मकNegative

Step 1

Concept

In this interval the first two factors are positive and the third is negative, so the product is negative. Tip: check factor signs separately.

Step 2

Why this answer is correct

The correct answer is B. ऋणात्मक / Negative. In this interval the first two factors are positive and the third is negative, so the product is negative. Tip: check factor signs separately.

Step 3

Exam Tip

इस अंतराल में पहले दो कारक धनात्मक और तीसरा ऋणात्मक है, इसलिए गुणनफल ऋणात्मक है। टिप: कारकों के चिह्न अलग-अलग जाँचें।

Open Question Page
Ask Friends

यदि (p(x)=-(x-2)(x+6)) है, तो (x<-6) के लिए ग्राफ (x)-अक्ष के किस ओर होगा?

If (p(x)=-(x-2)(x+6)), on which side of the (x)-axis will the graph lie for (x<-6)?

Explanation opens after your attempt
Correct Answer

B. नीचेBelow

Step 1

Concept

For (x<-6), both factors are negative and the outside negative makes the value negative. Tip: first check factor signs and then apply the outside sign.

Step 2

Why this answer is correct

The correct answer is B. नीचे / Below. For (x<-6), both factors are negative and the outside negative makes the value negative. Tip: first check factor signs and then apply the outside sign.

Step 3

Exam Tip

(x<-6) पर दोनों कारक ऋणात्मक हैं और बाहर का ऋण चिन्ह मान को ऋणात्मक बनाता है। टिप: पहले कारकों का चिह्न देखें फिर बाहरी चिन्ह लगाएं।

Open Question Page
Ask Friends

यदि (p(x)=(x+2)(x-1)(x-6)) है, तो (1<x<6) में (p(x)) का चिह्न क्या होगा?

If (p(x)=(x+2)(x-1)(x-6)), what will be the sign of (p(x)) for (1<x<6)?

Explanation opens after your attempt
Correct Answer

B. ऋणात्मकNegative

Step 1

Concept

In this interval the first two factors are positive and the third is negative, so the product is negative. Tip: check the sign of each factor separately.

Step 2

Why this answer is correct

The correct answer is B. ऋणात्मक / Negative. In this interval the first two factors are positive and the third is negative, so the product is negative. Tip: check the sign of each factor separately.

Step 3

Exam Tip

इस अंतराल में पहले दो कारक धनात्मक और तीसरा ऋणात्मक है, इसलिए गुणनफल ऋणात्मक है। टिप: प्रत्येक कारक का चिह्न अलग जांचें।

Open Question Page
Ask Friends

बहुपद (p(x)=(x-4)(x+2)) के आलेख के (x)-अक्ष कटान कौन से होंगे?

What will be the (x)-axis intersections of the graph of (p(x)=(x-4)(x+2))?

Explanation opens after your attempt
Correct Answer

A. ((4,0)) और ((-2,0))((4,0)) and ((-2,0))

Step 1

Concept

Setting the factors to zero gives (x=4) and (x=-2). Tip: convert each zero into the point ((x,0)).

Step 2

Why this answer is correct

The correct answer is A. ((4,0)) और ((-2,0)) / ((4,0)) and ((-2,0)). Setting the factors to zero gives (x=4) and (x=-2). Tip: convert each zero into the point ((x,0)).

Step 3

Exam Tip

कारकों को शून्य करने पर (x=4) और (x=-2) मिलते हैं। टिप: शून्यक को ((x,0)) बिंदु में बदलें।

Open Question Page
Ask Friends