# MCQs for NCERT Class 9 Mathematics Chapter 2 Polynomials

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. px3 + qx2 + 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 5x2 – (3 + k)x + 7 is zero, then zeroes of the polynomial 2x2 – 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) = 2x3 – 3x2 + 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 x2 + 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) = x3 + 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) x3 – 3x2 – 8x – 4
(B) x3 + 3x2 – 8x – 4
(C) x3 + 3x2 + 8x – 4
(D) x3 – 3x2 – 8x + 4

Ans.

C

Question. If p, q are the zeroes of the polynomial f(x) = x2 + 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 x3 – 3x2 + 3x + 5 is divided by x2 – 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 27x3 + 8y3 + 54x2y + 36xy2. 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) 4x3 – 13x + 6
(B) x3+ x+ x + 4
(C) 4x3 + 13x – 25
(D) – 2x3 + x– 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 x1/3+y1/3+z1/3 = 0 then which one of the following expression is correct :
(A) x+ y3+ z3 = 0
(B) x + y + z = 3x1/3+y1/3+z1/3
(C) x + y + z = 3xyz
(D) x+ y3+ z= 3xyz

Ans.

B

Question. Degree of the polynomial (x– 2) (x+ 11) is :
(A) 6
(B) 5
(C) 3
(D) 2

Ans.

B

Question. Which of the following is a binomial in y ?
(A) y2 + √2
(B) y + 1/y +2
(C) √y + √2y
(D) y√y + 1

Ans.

A

Question. If x+ 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 10x2 – 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– (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) = 6x3 + 11x2 – 39x – 65 so that f(x) is exactly divisible by x2 + 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) = (k2 + 4) x2 + 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 ax5 + bx3 + cx2 + 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 2x2 – 7x + 8β = 0, then the equation whose roots are(3α – 4β) and (3β – 4α) is _______.
(A) 2x2 + 7x + 98 = 0
(B) x2 + 7x + 98 = 0
(C) 2x2 – 7x – 98 = 0
(D) 2x2 – 7x + 98 = 0

Ans.

A

Question. For x2 + 2x + 5 to be a factor of x4 + αx2 + 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 ax2 + bx – c = 0, then find the value of

Ans.

D

Area of a triangular field is (x4 – 6x3 – 26x2 + 138x – 35) m2 and base of the triangular field is (x2 – 4x + 1) m. Find the height of the triangular field.
(A) 2(x2 – 2x – 35) m
(B) 1/2 (x2 − 2x − 35) m
(C) 2(3x2 – x – 4) m
(D) 1/2(3x2 − x − 4) m

Ans.

A

Question. A r e c t angular garden o f length (2x3 + 5x2 – 7) m has the perimeter (4x3 – 2x2 + 4) m. Find the breadth of the garden.
(A) (6x2 – 9) m
(B) (–6x2 + 9) m
(C) (2x3 – 7x2 + 11) m
(D) (6x3 + 7x2 + 9) m

Ans.

B

Question. Raghav had `(6x3 + 2x2 + 3x) and he bought (4x2 + 3) shirts. The price of each shirt is `(x + 5). How much money is left with Raghav?
(A) `(2x3 – 18x2 – 15)
(B) `(4x2 + 2x + 3)
(C) `(x3 – 3x)
(D) `(2x3 + 2x2 – 15)

Ans.

A

Question. Two different container contains (2x3 + 2x2 + 3x + 3) L and (4x3 – 2x2 + 6x – 3)L water. What is biggest measure that can measure both quantities exactly?
(A) (x2 + 2x) L
(B) (2x2 + 3) L
(C) (2x – 1) L
(D) (x + 1) L

Ans.

B

Question. Length and breadth of a rectangular park are (3x2 + 2x) m and (2x3 – 3) m respectively. Find the area of the park, when x = 3.
(A) 1924 m2
(B) 1492 m2
(C) 1881 m2
(D) 1683 m2

Ans.

D

Question. Find the roots of ax2 + bx + 6, if the polynomial x4 + x3 + 8x2 + ax + b is exactly divisible by x2 + 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 4x5 + 3x3 + 2x2 + 8 is divided by 4x2 + 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) = 3x4 + 6x3 – 2x2 – 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) = (k2 + 4)x2 + 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) = 2x3 + kx2 + 4x + 5
(R) If the polynomial f(x) = ax3 + bx – c                        (iii) –6
is exactly divisible by g(x) = x2 + 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 + Mx3 + Nx2 + 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) = x2 – 4x – 6 to make 5a a zero of the polynomial.
Reason (R): p(5) = 52 – 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): x4– y4 = (x – y) (x + y) (x2+ y2
(R): x2+ y2 = (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 2x3 – 5x2 + 2x – 18.
Reason (R) : 2(3)3 – 5(3)2 + 2(3) – 18 = 0.

Ans.

C

Question. (a): (x + 2y + z)2 = x+ 2y2 + z2 + 4xy + 2xz + 4yz.
(R): Identity is: (a + b + c)2 = a2+ b2 + c+ 2ab + 2bc + 2ca

Ans.

D

Question. Assertion (a): If x = 3/2 is a zero of the polynomial 2x2 + 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): 4x2 – 9y2 = (2x + 3y)(2x – 3y).
(R): 4x2 = (2x)2 and 9y2 = (3y)2

Ans.

B

Question. Assertion (a): (x – 1) is a factor of x+ x – 2.
Reason  (R): Coefficient of x is 1.

Ans.

B

Case based MCQs

Three friends A, B and C of locality decided to start a business with a capital represented by a polynomial x+ kx2 – 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
(D) cubic polynomial

Ans.

D

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  x12 – y12, 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 x12 – y12 is
(A) (x – y) (x + y) (x+ y2 + xy) (x4 + y4 – x2y2)
(B) (x – y) (x+ y– xy) (x4 + y4 – x2y2)
(C) (x + y) (x – y) (x2+ y2) (x+ y2– xy) (x+ y+ xy) (x4 + y4 – x2y2)
(D) (x + y) (x – y) (x+ y2) (x+ y2– xy) (x4 + y4 + x2y2

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