Students can refer to the following Polynomials Class 9 MCQ Questions with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here collection of multiple choice questions for Maths Polynomials Class 9 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

## Polynomials Class 9 MCQ Questions with Answers

We have provided below chapter wise Polynomials Class 9 MCQ Questions with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Maths Polynomials MCQs in Class 9 pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

**Question. If p(x) = x + 3, then p(x) + p(-x) is equal to**(a) 2x

(b) 3

(c) 0

(d) 6

**Answer**

D

**Question. If x+y+z = 0, then x ^{3}+y^{3}+z^{3} is**(a) 3xyz

(b) xyz

(c) 2xyz

(d) 0

**Answer**

A

**Question. The degree of constant function is**(a) 0

(b) 3

(c) 1

(d) 2

**Answer**

A

**Question. (x + 1) is a factor of the polynomial**(a) x

^{3}+x

^{2}-x+1

(b) x

^{2}+x

^{3}+x+1

(c) x

^{4}+3x

^{3}+3x

^{2}+x+1

(d) x

^{4}+x

^{3}+x

^{2}+x+1

**Answer**

B

**Question. The coefficient of ‘x’ in the expansion of(x+3) ^{3} is**(a) 1

(b) 27

(c) 9

(d) 18

**Answer**

B

**Question. Which of these is a zero of the polynomial p(y) = 3y ^{3} – 16y – 8 ?**

(a) – 8

(b) – 2

(c) 0

(d) 2

**Answer**

B

**Question. Which of the following is a polynomial in x ?**

(a) x + 1/x

(b) x^{2 }+ √x

(c) x +√2x^{2} + 1

(d) √3x+ 1

**Answer**

C

**Question. Which of the following is a quadratic polynomial ?**

(a) x + 2

(b) x^{2 }+ 2

(c) x^{3 }+ 2

(d) 2x + 2

**Answer**

B

**Question. The value of p for which x + p is a factor of x ^{2}+ px + 3 – p is :**

(a) 1

(b) – 1

(c) 3

(d) – 3

**Answer**

C

**Question. The polynomial (4x – 3)is a factor of the polynomial q(x) = 4x ^{3} + x^{2 }– 11x + 2r. What is the value of r ? **

(a) 2

(b) 3

(c) 4

(d) 11

**Answer**

B

**Question. The polynomial p(x) = x ^{3} – 5x^{2}– x + 5 is such that p(1) = 0 and p(– 1) = 0. Which of these is equivalent to p(x) ?**

(a) (x – 1)(x + 5)

(b) (x – 1)(x + 1)(x + 5)

(c) (x – 1)(x + 1)(x – 5)

(d) (x + 1)(x – 5)

**Answer**

C

**Question. The maximum number of terms in a polynomial of degree 10 is :**

(a) 9

(b) 10

(c) 11

(d) 1

**Answer**

C

**Question. Degree of zero polynomial is : **

(a) 0

(b) 1

(c) any natural number

(d) not defined

**Answer**

D

**Question. The coefficient of x ^{2 }in (3x + x^{3}) (x + 1/x) is :**

(a) 3

(b) 1

(c) 4

(d) 2

**Answer**

C

**Question. Which of the following is not a polynomial?**

(a) 3

(b) 3x^{2} + √5x

(c) x^{2 }+1/x^{2 } – 4

(d) πt^{7} – 3t^{2} + 4

**Answer**

C

**Question. Degree of which of the following polynomials is zero :**

(a) x

(b) 15

(c) y

(d) x + x^{2 }

**Answer**

B

**Question. Which of the following is a cubic polynomial?**

(a) x^{3 }+ 3x^{2} – 4x + 3

(b) x^{2}+ 4x – 7

(c) 3x^{2 }+ 4

(d) 3(x^{2 } + x + 1)

**Answer**

A

**Question. The coefficient of x in the expansion (x + 3) ^{3} is :**

(a) 1

(b) 9

(c) 18

(d) 27

**Answer**

D

**Question. A cubic polynomial is a polynomial with degree :**

(a) 1

(b) 3

(c) 0

(d) 2

**Answer**

B

**Question. Consider the expression x ^{(m2-1)} + 3x^{m/2} where m is a constant. For what value of m, will the expression be a cubic polynomial?**

(a) – 2

(b) – 1

(c) 1

(d) 2

**Answer**

D

**Question. Fill in the blanks: A polynomial containing one non-zero term is called a ________.**

**Answer**

monomial

**Question. Fill in the blanks: The highest power of the variable in a polynomial is called the ________ of the polynomial.**

**Answer**

degree

**Question. Write (-3x + y + z)2 in the expanded form:**

## Answer

We have,

(-3x + y + z)^{2}

Using identity (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc + 2ca

= (-3x)^{2} + y^{2} + z^{2} + 2 (-3x) y + 2 y z + x 2 x (-3x)

= 9x^{2} + y^{2} + z^{2} – 6xy + 2yz – 6zx

**Question. Evaluate the following by using identities: 0.54×0.54 – 0.46×0.46**

## Answer

We have,

0.54 x 0.54 – 0.46 x 0.46

= (0.54)^{2} – (0.46)^{2} = (0.54 + 0.46)(0.54 – 0.46) = 1 x 0.08 = 0.08

**Question. Evaluate: 185×185 – 15×15**

## Answer

185 x 185 – 15 x 15

(185)^{2} – (15)^{2} [Using a^{2} – b^{2} -(a – b)(a + b) ]

(185 + 15)(185 – 15)

200 x 170 = 34000

**Question. Evaluate 105×108 without multiplying directly.**

**Answer**

11. 105×108=(100+5)(100+8)

Using identity (x+a)(x+b)=x2+(a+b)x+ab

We get, 105×108 = 100^{2} + (5 + 8)100 + 5×8

=10000+1300+40=11340

**Question. Simplify (x + y) ^{3} – (x – y)^{3} – 6y(x + y) (x – y).**

## Answer

(x + y)^{3} – (x – y)^{3} – 6y(x + y)(x – y)

= (x + y)^{3} – (x – y)^{3} – 3.2y(x + y)(x – y)

= (x + y)^{3} – (x – y)^{3} – 3 (x + y – x + y)(x + y)(x – y)

= [x + y – x + y)]^{3} [∴a^{3} – b^{3} – 3ab(a – b) = (a – b)^{3}]

=(2y)^{3} = 8y^{3}

**Question**.** Factorize : (a ^{2} – b^{2})^{3} + (b^{2} – c^{2})^{3} + (c^{2} – a^{2})^{3}**

## Answer

Let x = a^{2} – b^{2}, y = b^{2} – c^{2} and z = c^{2} – a^{2}. Then,

x + y + z = a^{2} – b^{2} + b^{2} – c^{2} + c^{2} – a^{2} = 0

x^{3} + y^{3} + z^{3} = 3xyz

⇒(a^{2} – b^{2})3 + (b^{2} – c^{2})3 + (c^{2} – a^{2})3 = 3(a^{2} – b^{2})(b^{2} – c^{2})(c^{2} – a^{2})

⇒(a^{2} – b^{2})3 + (b^{2} – c^{2})^{3} + (c^{2} – a^{2})^{3} = 3(a + b)(a – b)(b + c)(b – c)(c + a)(c – a)

⇒(a^{2} – b^{2})^{3} + (b^{2} – c^{2})^{3} + (c^{2} – a^{2})^{3} = 3(a + b)(b + c)(c + a)(a – b)(b – c)(c – a)

**Question**. **If both x – 2 and x-1/2 are factors of px2 + 5x + r, show that p = r.**

## Answer

Let f(x) = px2 + 5x + r be the given polynomial. Since x – 2 and x-1/2 are factors of f(x).

f(2) = 0 and f(1/2) = 0

⇒pX2^{2} + 5X2 + r = 0 and p(1/2)^{2} + 5X1/2 + r = 0

⇒4p + 10 + r = 0 and P/4+5/2 + r = 0

⇒4p + r = -10 and p+4r+10/4

⇒4p + r = -10 and p + 4r + 10 = 0

⇒4p + r = -10 and p + 4r = -10

⇒4p + r = p + 4r [RHS of the two equations are equal]

⇒3p = 3r⇒p = r

**Question**.** If the polynomials az ^{3} + 4z^{2} + 3z – 4 and z^{3} – 4z + a leave the same remainder when divided by z – 3, find the value of a.**

**Answer**

.Let p(z) = az^{3} + 4z^{2} + 3z – 4

And q(z) = z^{3} – 4z + a

As these two polynomials leave the same remainder, when divided by z – 3, then p(3) =

q(3).

p(3) = a(3)^{3} + 4(3)^{2} + 3(3) – 4

= 27a + 36 + 9 – 4

Or p(3) = 27a + 41

And q(3) = (3)^{3} – 4(3) + a

= 27 – 12 + a = 15 + a

Now, p(3) = q(3)

⇒27a + 41 = 15 + a

⇒26a = -26; a = -1

Hence, the required value of a = -1.

**Case based MCQs**

**Read the following passage and answer the questions.**

Teacher wrote of polynomial x^{2} + kx + 8 on the blackboard and said that value of this polynomial at x = –3 is –1.

**Question. Value of the polynomial at x = –5 is**

(a) –3

(b) 3

(c) –7

(d) 7

**Answer**

B

**Question. Value of the polynomial at x = 3 is**

(a) 1

(b) 18

(c) 25

(d) 35 D

**Answer**

D

**Question. What type of polynomial is it? **

**Answer**

Quadratic

**Question. Value of k is**

(a) 6

(b) –6

(c) 9

(d) –9

**Answer**

A

**Question. Zeroes of this polynomial are**

(a) 4 and 2

(b) 4 and –2

(c) –4 and 2

(d) –4 and –2

**Answer**

D

**Read the following passage and answer the questions.**

Teacher asked the students to state the value of ‘a’, if on dividing the polynomial y^{3} – 4y + a by (y – 3), remainder is 31.

**Question. What will be the remainder, if the polynomial is divided by (x + 2)? **

(a) 32

(b) 16

(c) 12

(d) 8

**Answer**

B

**Question. Which of the following responses of the students is correct?**

(a) 16

(b) 13

(c) –13

(d) –16

**Answer**

A

**Question. What will be remainder if the polynomial is divided by (x – 5)?**

(a) 115

(b) 117

(c) 119

(d) 121

**Answer**

D

**Question. What type of a polynomial is it? **

**Answer**

Cubic

**Question. What will be the remainder, if the polynomial is divided by (x + 5)?**

(a) – 87

(b) – 89

(c) – 91

(d) – 93

**Answer**

B

Our teachers have developed really good **Multiple Choice Questions** covering all important topics in each chapter which are expected to come in upcoming tests and exams, as MCQs are coming in all exams now therefore practice them carefully to get full understanding of topics and get good marks. Download the latest questions with multiple choice answers for Class 9 Maths Polynomials in pdf or read online for free.

The above **NCERT based MCQs for Class 9 Maths Polynomials have** been designed by our teachers in such a way that it will help you a lot to gain an understanding of each topic. These CBSE NCERT Class 9 Maths Polynomials Multiple Choice Questions have been developed and are available free for benefit of Class 9 students.

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