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

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

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

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

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

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

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

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

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

Question. In which of the following, (x + 2) is a factor ?
(A) 4x³ – 13x + 6
(B) x³+ x² + x + 4
(C) 4x³ + 13x – 25
(D) – 2x³ + x² – x – 19

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

Question. If x^1/3+y^1/3+z^1/3 = 0 then which one of the following expression is correct :
(A) x³ + y³+ z³ = 0
(B) x + y + z = 3x^1/3+y^1/3+z^1/3
(C) x + y + z = 3xyz
(D) x³ + y³+ z³ = 3xyz

Question. Degree of the polynomial (x³ – 2) (x² + 11) is : 
(A) 6
(B) 5
(C) 3
(D) 2

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

Question. If x² + kx + 6 + (x + 2)(x + 3) for all x, the value of k is :
(A) 1
(B) – 1
(C) 5
(D) 3

Question. 8 is a polynomial of degree :
(A) 1
(B) 1/2
(C) 8
(D) 0

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)

Question. The zeroes of the polynomial p(x) = x² – (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)

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

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

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

Question. A polynomial of the form ax⁵ + bx³ + cx² + dx + e has at most _______ zeroes.
(A) 3
(B) 5
(C) 7
(D) 11

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

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

Question. If α, β be two zeroes of the quadratic polynomial ax² + bx – c = 0, then find the value of

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

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

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

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

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

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

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

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

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)

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

Question. The degree of a non-zero constant polynomial is :
(A) 1
(B) –1
(C) 0
(D) –2

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. 

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

Question. (a): x⁴– y⁴ = (x – y) (x + y) (x²+ y²) 
(R): x²+ y² = (x – y) (x + y) 

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

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. 

Question. (a): (x + 2y + z)² = x² + 2y² + z² + 4xy + 2xz + 4yz.
(R): Identity is: (a + b + c)² = a²+ b² + c² + 2ab + 2bc + 2ca 

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. 

Question. (a): 4x² – 9y² = (2x + 3y)(2x – 3y).
(R): 4x² = (2x)² and 9y² = (3y)². 

Question. Assertion (a): (x – 1) is a factor of x² + x – 2.
Reason  (R): Coefficient of x is 1. 

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 x³ + 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) 

Question. Share of C in the capital is
(A) (x – 1)
(B) (x – 3)
(C) (x – 5)
(D) (x + 5)

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 

Question. If x = 20, then total capital (in ) is
(A) 10025
(B) 10005
(C) 9995
(D) 9985 

Question. The polynomial is a 
(A) constant polynomial
(B) linear polynomial
(C) quadratic polynomial
(D) cubic polynomial 

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  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) (x² + y² + xy) (x⁴ + y⁴ – x²y²)
(B) (x – y) (x² + y² – xy) (x⁴ + y⁴ – x²y²)
(C) (x + y) (x – y) (x²+ y²) (x² + y²– xy) (x² + y² + xy) (x⁴ + y⁴ – x²y²)
(D) (x + y) (x – y) (x² + y²) (x² + y²– xy) (x⁴ + y⁴ + x²y²) 

Question. If x = 2 and y = 1, then the total contribution (in ) is
(A) 4195
(B) 4095
(C) 4083
(D) 3993 

Question. Number of students, who contributed the money, is
(A) 3
(B) 4
(C) 5
(D) 6 

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

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