MCQ Chapter 2 Polynomials Class 9 Mathematics

Please refer to Polynomials MCQ Questions Class 9 Mathematics below. These MCQ questions for Class 9 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Polynomials will help you to prepare for the exams and get more marks.

Polynomials MCQ Questions Class 9 Mathematics

Please see solved MCQ Questions for Polynomials in Class 9 Mathematics. All questions and answers have been prepared by expert faculty of standard 9 based on the latest examination guidelines.

MCQ Questions Class 9 Mathematics Polynomials

Question. (x + y)³ – (x – y)³ – 6y(x² – y² ) =
(a) y³
(b) 2y³ 
(c) 4y³ 
(d) 8y³

Question. Factorise: x²+ (a + b + c)x + ab + bc
(a) (x + a)(x + b + c)
(b) (x + a)(x + a + c)
(c) (x + b)(x + a + c)
(d) (x + b)(x + b + c)

Question. If p(x) = x¹⁶⁰ + 2x¹⁴¹ + k and p(–1) = 0, then the value of k is
(a) 1
(b) – 3
(c) 2
(d) – 2

Question. If a³ + b³ + c³ = 3abc, then a² / bc + b² / ca + c² / ab =
(a) 0
(b) 1
(c) – 1
(d) 3

Question. If x = –2 and x²+ y² + 3xy = –5, then find y.
(a) –2
(b) 3
(c) – 4
(d) 9

Question. The factors of x³ + 9x² + 23x + 15 are
(a) (x + 1), (x + 3), (x + 5)
(b) (x + 1), (x + 3), (x – 5)
(c) (x + 1), (x – 3), (x – 5)
(d) (x – 1), (x – 3), (x – 5)

Question. The value of (369)² – (368)² is
(a) 12
(b) 81
(c) 37
(d) 737

Question. If p(y) = y² – y + 1, then find the value of p(0) – p(1).
(a) 1
(b) 3
(c) 0
(d) 2

Question. Factors of polynomial 12x² + 7x + 1 are
(a) (3x – 1)(4x + 1)
(b) (3x – 1)(4x – 1)
(c) (4x – 1)(3x– 1)
(d) (4x + 1)(3x + 1)

Question. If a + b + c = 13 and ab + bc + ca = 84, then find the value of a² + b² + c².
(a) 1
(b) 2
(c) 3
(d) 4

Question. One of the zeroes of the polynomial 2x² + 7x – 4 is
(a) 2
(b) 1/2
(c) − 1/2
(d) – 2

Question. The value of (9)³ + (– 3)³ is
(a) – 81
(b) 54
(c) 164
(d) 702

Question. Simplify : x³ – 4 – x + 4x² / x² + 3x – 4
(a) 4 + x
(b) 2 + x
(c) 1 – x
(d) x + 1

Question. If p(x) = x⁵¹ + 51, then value of p(–1) is
(a) 0
(b) 1
(c) 49
(d) 50

Question. Using algebraic identity, find the value of 209 × 191.
(a) 39851
(b) 39919
(c) 39961
(d) 38951

Question. The degree of the polynomial (y³ – 3)(y²+ 8) is
(a) 2
(b) 3
(c) 0
(d) 5

Question. The coefficient of the highest power of x in the polynomial 3x³ – 4x⁴ + 5x² – 2x⁵ + 3 is
(a) 2
(b) – 4
(c) 3
(d) –2

Assertion & Reasoning Based MCQs

(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : The degree of the polynomial (x² – 2)(x – 3)(x + 4) is 3.
Reason : A polynomial of degree 3 is called a cubic polynomial.

Question. Assertion : 3x² + x – 1 = (x + 1) (3x – 2) + 1.
Reason : To factorise ax² + bx + c, write b as sum of two numbers whose product is ac.

Question. Assertion : The value of (–27)³ + (–9)³ is –20412.
Reason : If a + b = 0, then a³ + b³ + c³ = 0

Question. Assertion : If 2x² – 32 is the volume of a cuboid, then length of cuboid can be x – 8.
Reason : Volume of a cuboid = l × b × h.

Question. Assertion : The expression 3×4 – 4x^3/2 + x² = 2 is not a polynomial because the term – 4x^3/2 contains a rational power of x.
Reason : The highest exponent in various terms of an algebraic expression in one variable is called its degree.

Question. Assertion : If x = 3/2 is a zero of polynomial 2x² + kx – 12, then k = 5.
Reason : If x = a is zero of a polynomial f(x), then f(a) = 0.

Question. Assertion : –7 is a constant polynomial.
Reason : Degree of a constant polynomial is zero.

Question. Assertion : The value of 593 × 607 is 359951.
Reason : (a + b) (a – b) = a² – b²

Fill in the blanks:

Question. If (x – 1) is a factor of x² + x + k, then value of k is ______. 

Question. Coefficient of x² in the polynomial π/4x² – 3x + 4 is ______.

Question. Zero of the polynomial p(x) = 2x + 3 is ______. 

Question. If x/y + y/x = –1 , (x ≠ 0, y ≠ 0), then the value of x³ – y³  is______.

Question. If x –1/x = 3 , then value of x³ – 1/ x³ s _____ .

Question. Degree of a linear polynomial is______ . 

True /False:

Question. If p(x) = x²+ 3x + 2, then p(1) + p(2) + p(0) is 18.

Question. Degree of the polynomial 2 – x² – 3x³ + 2x⁷ is 7. 

Question. (x + 1) is a factor of x¹⁴⁰ + 2x¹⁴¹ + 2. 

Question. Zeroes of a polynomial 3(x – 2) (x + 3) are 2 and 3. 

Question. Degree of the zero polynomial is zero.

Question. Zero of a zero polynomial is any real number. 

Question. (x – 3) is a factor of 2x³ – 5x² + 2x – 18. 

Case Based MCQs

Read the following passage and answer the questions.
Ankur and Ranjan start a new business together. The amount invested by both partners together is given by the polynomial p(x) = 4x² + 12x + 5, which is the product of their individual shares.

Question. Total amount invested by both, if x = 1000 is
(a) Rs 301506
(b) Rs 370561
(c) Rs 4012005
(d) Rs 490621

Question. The shares of Ankur and Ranjan invested individually are
(a) Rs (2x + 1), Rs (2x + 5)
(b) Rs (2x + 3), Rs (x + 1)
(c) Rs (x + 1), Rs (x + 3)
(d) None of these

Question. Find the value of x, if the total amount invested is equal to 0.
(a) –1/2
(b) –5/2
(c) Both (a) and (b)
(d) None of these

Question. Coefficient of x² in the given polynomial is
(a) 2
(b) 3
(c) 4
(d) 12

Question. Name the polynomial of amounts invested by each partner.
(a) Cubic
(b) Quadratic
(c) Linear
(d) None of these