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factor form MCQ Questions for Class 10

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Practice Questions

15 questions tagged with factor form.

Question 1/15 Expert Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

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।

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Question 2/15 Expert Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

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।

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Question 3/15 Expert Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

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।

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Question 4/15 Expert Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

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।

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Question 5/15 Expert Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

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।

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Question 6/15 Expert Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

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।

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Question 7/15 Expert Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

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।

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Question 8/15 Expert Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

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।

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Question 9/15 Hard Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

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।

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Question 10/15 Hard Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24

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।

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Question 11/15 Hard Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

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।

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Question 12/15 Hard Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23

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।

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Question 13/15 Hard Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

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।

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Question 14/15 Hard Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

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।

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Question 15/15 Medium Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

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।

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