Please refer to the MCQ Questions for Class 9 Mathematics Chapter 2 Polynomials with Answers. The following Polynomials Class 9 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 9. Our experts have designed MCQ Questions for Class 9 Mathematics with Answers for all chapters in your NCERT Class 9 Mathematics book.

## Polynomials Class 9 MCQ Questions with Answers

See below Polynomials Class 9 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question. px ^{3} + qx^{2} + rx + s = 0 is said to be cubic polynomial, if _______.**

(A) s ≠ 0

(B) r ≠ 0

(C) q ≠ 0

(D) p ≠ 0

## Ans.

D

**Question. If sum of all zeros of the polynomial 5x ^{2} – (3 + k)x + 7 is zero, then zeroes of the polynomial 2x^{2} – 2(k + 11)x + 30 are**

(A) 3, 5

(B) 7, 9

(C) 3, 6

(D) 2, 5

## Ans.

A

**Question. If the sum of the product of the zeroes taken two at a time of the polynomial f(x) = 2x ^{3} – 3x^{2} + 4tx – 5 is –8, then the value of t is _______.**

(A) 2

(B) 4

(C) –2

(D) – 4

## Ans.

D

**Question. If a and b are the roots of the quadratic equation x ^{2} + px + 12 = 0 with the condition a – b = 1, then the value of ‘p’ is _______.**

(A) 1

(B) 7

(C) –7

(D) 7 or –7

## Ans.

D

**Question. What will be the value of p(3), if 3 is one of zeroes of polynomial p(x) = x ^{3} + bx + D?**

(A) 3

(B) D

(C) 27

(D) 0

## Ans.

D

**Question. A cubic polynomial with sum of its zeroes, sum of the product of its zeroes taken two at a time and the product of its zeroes as –3, 8, 4 respectively, is _______.**

(A) x^{3} – 3x^{2} – 8x – 4

(B) x^{3} + 3x^{2} – 8x – 4

(C) x^{3} + 3x^{2} + 8x – 4

(D) x^{3} – 3x^{2} – 8x + 4

## Ans.

C

**Question. If p, q are the zeroes of the polynomial f(x) = x ^{2} + k(x – 1) – c, then (p – 1)(q – 1) is equal to _______.**

(A) c –1

(B) 1 – c

(C) c

(D) 1 + c

## Ans.

B

**Question. When x ^{3} – 3x^{2} + 3x + 5 is divided by x^{2} – x + 1, the quotient and remainder are _______.**

(A) x + 2, 7

(B) x – 2, –7

(C) x – 2, 7

(D) x + 2, –7

## Ans.

C

**Question. The volume of a cube is given by the expression 27x ^{3} + 8y^{3} + 54x^{2}y + 36xy^{2}. What is the expression for the side length of the cube?**

(A) 3x + 2y

(B) 3x – 2y

(C) 9x – 8y

(D) 9x + 8y

## Ans.

A

**Question. In which of the following, (x + 2) is a factor ?**

(A) 4x^{3} – 13x + 6

(B) x^{3}+ x^{2 }+ x + 4

(C) 4x^{3} + 13x – 25

(D) – 2x^{3} + x^{2 }– x – 19

## Ans.

A

**Question. The factorisation of (2a – b) ^{3} + (b – 2c)^{3} + 8(c – a)^{3} is :**

(A) (2a – b)(b – 2c)(c – a)

(B) 3(2a – b)(b – 2c)(c – a)

(C) 6(2a – b)(b – 2c)(c – a)

(D) 2a × b × 2c

## Ans.

C

**Question. If x ^{1/3}+y^{1/3}+z^{1/3} = 0 then which one of the following expression is correct :**

(A) x

^{3 }+ y

^{3}+ z

^{3}= 0

(B) x + y + z = 3x

^{1/3}+y

^{1/3}+z

^{1/3}

(C) x + y + z = 3xyz

(D) x

^{3 }+ y

^{3}+ z

^{3 }= 3xyz

## Ans.

B

**Question. Degree of the polynomial (x ^{3 }– 2) (x^{2 }+ 11) is : **

(A) 6

(B) 5

(C) 3

(D) 2

## Ans.

B

**Question. Which of the following is a binomial in y ?**

(A) y^{2} + √2

(B) y + 1/y +2

(C) √y + √2y

(D) y√y + 1

## Ans.

A

**Question. If x ^{2 }+ kx + 6 + (x + 2)(x + 3) for all x, the value of k is :**

(A) 1

(B) – 1

(C) 5

(D) 3

## Ans.

C

**Question. 8 is a polynomial of degree :**

(A) 1

(B) 1/2

(C) 8

(D) 0

## Ans.

D

**Question. Which of these is obtained by factorizing the polynomial 10x ^{2} – 9x + 2 ?**

(A) (2x – 1)(5x – 2)

(B) (2x – 1)(5x + 2)

(C) (2x + 1)(5x + 2)

(D) (2x + 1)(5x – 2)

## Ans.

A

**Question. The zeroes of the polynomial p(x) = x ^{2 }– (2k + 1)x + 16 are positive integers. Given that k is an integer, which of these is equivalent to the polynomial?**

(A) (x – 1)(x + 16)

(B) (x – 1)(x – 16)

(C) (x – 2)(x – 8)

(D) (x – 4)(x – 4)

## Ans.

B

**Question. What should be subtracted from f(x) = 6x ^{3} + 11x^{2} – 39x – 65 so that f(x) is exactly divisible by x^{2} + x – 1?**

(A) 38x + 60

(B) –38x – 60

(C) –19x – 30

(D) 9x + 10

## Ans.

B

**Question. Which of the following graph has more than three distinct real roots?**

## Ans.

C

**Question. If one zero of the polynomial f(x) = (k ^{2} + 4) x^{2} + 13x + 4k is reciprocal of the other, then k is equal to _______.**

(A) 2

(B) –2

(C) 1

(D) –1

## Ans.

A

**Question. A polynomial of the form ax ^{5 }+ bx^{3} + cx^{2} + dx + e has at most _______ zeroes.**

(A) 3

(B) 5

(C) 7

(D) 11

## Ans.

B

**Question. If α and β are the roots of the equation 2x ^{2} – 7x + 8β = 0, then the equation whose roots are(3α – 4β) and (3β – 4α) is _______.**

(A) 2x

^{2}+ 7x + 98 = 0

(B) x

^{2}+ 7x + 98 = 0

(C) 2x

^{2}– 7x – 98 = 0

(D) 2x

^{2}– 7x + 98 = 0

## Ans.

A

**Question. For x ^{2} + 2x + 5 to be a factor of x^{4} + αx^{2} + β, the values of a and b should respectively be _______.**

(A) 2, 5

(B) 5, 25

(C) 6, 25

(D) 5, 2

## Ans.

C

**Question. If α, β be two zeroes of the quadratic polynomial ax ^{2} + bx – c = 0, then find the value of**

## Ans.

D

**Area of a triangular field is (x ^{4} – 6x^{3 }– 26x^{2} + 138x – 35) m^{2} and base of the triangular field is (x^{2} – 4x + 1) m. Find the height of the triangular field.**

(A) 2(x

^{2}– 2x – 35) m

(B) 1/2 (x

^{2}− 2x − 35) m

(C) 2(3x

^{2}– x – 4) m

(D) 1/2(3x

^{2}− x − 4) m

## Ans.

A

**Question. A r e c t angular garden o f length (2x ^{3} + 5x^{2} – 7) m has the perimeter (4x^{3} – 2x^{2} + 4) m. Find the breadth of the garden.**

(A) (6x

^{2}– 9) m

(B) (–6x

^{2}+ 9) m

(C) (2x

^{3}– 7x

^{2}+ 11) m

(D) (6x

^{3}+ 7x

^{2}+ 9) m

## Ans.

B

**Question. Raghav had `(6x ^{3 }+ 2x^{2} + 3x) and he bought (4x^{2} + 3) shirts. The price of each shirt is `(x + 5). How much money is left with Raghav?**

(A) `(2x

^{3}– 18x

^{2}– 15)

(B) `(4x

^{2}+ 2x + 3)

(C) `(x

^{3}– 3x)

(D) `(2x

^{3}+ 2x

^{2}– 15)

## Ans.

A

**Question. Two different container contains (2x ^{3} + 2x^{2} + 3x + 3) L and (4x^{3} – 2x^{2} + 6x – 3)L water. What is biggest measure that can measure both quantities exactly?**

(A) (x

^{2}+ 2x) L

(B) (2x

^{2}+ 3) L

(C) (2x – 1) L

(D) (x + 1) L

## Ans.

B

**Question. Length and breadth of a rectangular park are (3x ^{2} + 2x) m and (2x^{3} – 3) m respectively. Find the area of the park, when x = 3.**

(A) 1924 m

^{2}

(B) 1492 m

^{2}

(C) 1881 m

^{2}

(D) 1683 m

^{2}

## Ans.

D

**Question. Find the roots of ax ^{2} + bx + 6, if the polynomial x4 + x^{3} + 8x^{2} + ax + b is exactly divisible by x^{2} + 1.**

(A) –1, 3

(B) 2, 5

(C) –1, –6

(D) –3, 2

## Ans.

C

**Question. Which of the following options hold? Statement – I : If p(x) and g(x) are two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that p(x) = g(x) × q(x) + r(x), where degree of r(x) is greater than degree of g(x). Statement – **II : When 4x

^{5}+ 3x

^{3}+ 2x

^{2}+ 8 is divided by 4x

^{2}+ 2x + 1, then degree of remainder is 1.

(A) Both Statement – I and Statement – II are true.

(B) Statement – I is true but Statement – II is false.

(C) Statement – I is false but Statement – II is true.

(D) Both Statement – I and Statement – II are false

## Ans.

C

**Question. Obtain all the zeroes of the polynomial f(x) = 3x ^{4} + 6x^{3} – 2x^{2} – 10x – 5, if two of its zeros are √5/3 and− √5/3**

(A) 1, –1

(B) 1, 1

(C) –1, –1

(D) 1, 0

## Ans.

C

**Question. Match the following.****Column – I Column – II**

(P) If one of the zero of the polynomial (i) 1

f(x) = (k^{2} + 4)x^{2} + 13x + 4

is reciprocal of the other, then k is equal to

(Q) Sum of the zeroes of the polynomial (ii) 0

is 3, then k is equal to f(x) = 2x^{3} + kx^{2} + 4x + 5

(R) If the polynomial f(x) = ax^{3 }+ bx – c (iii) –6

is exactly divisible by g(x) = x^{2} + bx + c,

then ab is equal to

(A) (P) → (iii); (Q) → (i); (R) → (ii)

(B) (P) → (ii); (Q) → (iii); (R) → (i)

(C) (P) → (i); (Q) → (iii); (R) → (ii)

(D) (P) → (ii); (Q) → (i); (R) → (iii)

## Ans.

B

**Question. If 1 and –1 are zeroes of polynomial Lx4 + Mx ^{3} + Nx^{2} + Rx + P, then Find :**

(i) L + N + P

(ii) M + R

(iii) M3 + R3

(i) (ii) (iii)

(A) 1 1 –1

(B) 0 –1 0

(C) 0 0 0

(D) –1 1 1

## Ans.

C

**Question. The degree of a non-zero constant polynomial is :**

(A) 1

(B) –1

(C) 0

(D) –2

## Ans.

C

**Assertion & Reasoning Based MCQs**

**(A) Both (a) and (R) are true and (R) is the correct explanation of (a).****(B) Both (a) and (R) are true but (R) is not the correct explanation of (a).****(C) (a) is true but (R) is false.****(D) (R) is true but (a) is false.**

**Question. Assertion (a): –1 must be added to the polynomial p(x) = x ^{2} – 4x – 6 to make 5a a zero of the polynomial.**

**Reason (R): p(5) = 5**

^{2}– 4 × 5 – 6 = –1.## Ans.

A

**Question. Assertion (a): (x – a) is a factor of p(x), if p(a) = 0.****Reason (R): Factor theorem. **

## Ans.

A

**Question. (a): x ^{4}– y^{4} = (x – y) (x + y) (x^{2}+ y^{2}) **

(R): x^{2}+ y^{2} = (x – y) (x + y)

## Ans.

C

**Question. Assertion (a): Zero of the polynomial 3x – 2 is 2/3 .****Reason (R): 3x – 2 = 0 ⇒ x = 2/3 . **

## Ans.

A

**Question. Assertion (a): (x – 3) is not a factor of 2x ^{3} – 5x^{2} + 2x – 18.**

**Reason (R) : 2(3)**

^{3}– 5(3)^{2}+ 2(3) – 18 = 0.## Ans.

C

**Question. (a): (x + 2y + z) ^{2} = x^{2 }+ 2y^{2} + z^{2} + 4xy + 2xz + 4yz.**

(R): Identity is: (a + b + c)^{2} = a^{2}+ b^{2} + c^{2 }+ 2ab + 2bc + 2ca

## Ans.

D

**Question. Assertion (a): If x = 3/2 is a zero of the polynomial 2x ^{2} + kx – 12, then the value of k is 5.**

**Reason (R): 2(3/2)**

^{2}+ k(3/2) – 12 = 1 gives k = 5.## Ans.

C

**Question. (a): 4x ^{2} – 9y^{2} = (2x + 3y)(2x – 3y).**

**(R): 4x**

^{2}= (2x)^{2}and 9y^{2}= (3y)^{2}.## Ans.

B

**Question. Assertion (a): (x – 1) is a factor of x ^{2 }+ x – 2.**

**Reason (R): Coefficient of x is 1.**

## Ans.

B

**Case based MCQs**

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

Three friends A, B and C of locality decided to start a business with a capital represented by a polynomial x^{3 }+ kx^{2} – x + 5, which is the product of their shares, such that shares of A, B and C are in decreasing order.

**Question. Share of B in the capital is**

(A) (x + 1)

(B) (x – 1)

(C) (x – 2)

(D) (x – 5)

## Ans.

B

**Question. Share of C in the capital is**

(A) (x – 1)

(B) (x – 3)

(C) (x – 5)

(D) (x + 5)

## Ans.

C

**Question. If share of A in the capital polynomial is (x + 1), then value of k is**

(A) 1

(B) –1

(C) 5

(D) –5

## Ans.

D

**Question. If x = 20, then total capital (in ) is**

(A) 10025

(B) 10005

(C) 9995

(D) 9985

## Ans.

D

**Question. The polynomial is a **

(A) constant polynomial

(B) linear polynomial

(C) quadratic polynomial

(D) cubic polynomial

## Ans.

D

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

Some of the students of class IX contributed some money to help in the education of needy students. Their total contribution is in the form of a polynomial x^{12} – y^{12}, which is the product of the contributions of all the students. These contributions are in the form of irreducible factors of the total contribution.

**Question. Factorisation of x ^{12} – y^{12} is**

(A) (x – y) (x + y) (x

^{2 }+ y

^{2}+ xy) (x

^{4}+ y

^{4}– x

^{2}y

^{2})

(B) (x – y) (x

^{2 }+ y

^{2 }– xy) (x

^{4}+ y

^{4}– x

^{2}y

^{2})

(C) (x + y) (x – y) (x

^{2}+ y

^{2}) (x

^{2 }+ y

^{2}– xy) (x

^{2 }+ y

^{2 }+ xy) (x

^{4}+ y

^{4}– x

^{2}y

^{2})

(D) (x + y) (x – y) (x

^{2 }+ y

^{2}) (x

^{2 }+ y

^{2}– xy) (x

^{4}+ y

^{4}+ x

^{2}y

^{2})

## Ans.

C

**Question. If x = 2 and y = 1, then the total contribution (in ) is**

(A) 4195

(B) 4095

(C) 4083

(D) 3993

## Ans.

B

**Question. Number of students, who contributed the money, is**

(A) 3

(B) 4

(C) 5

(D) 6

## Ans.

D

**Question. Which algebraic identities will help you in the process? **

## Ans.

a^{2} – b^{2} = (a + b) (a – b), a^{3} + b^{3} = (a + b) (a^{2} – ab + b^{2}) and a^{3 }– b^{3} = (a – b) (a^{2} + ab + b^{2})

**Question. How you will find the contribution of each student? **

## Ans.

By factorising x^{12} – y^{12}