Hope you have already attempted the chapter 1 questions. Now lets try solving the MCQ questions for chapter 2 Polynomials.
CBSE Class 9th Maths Important MCQs with Answers from Chapter 2 – Polynomials
Question 1. What is the degree of the polynomial 7x³ – 4x² + x – 2?
a) 1
b) 2
c) 3
d) 0
Answer:
c) 3 — The degree of a polynomial is the highest power of the variable, which here is 3 in the term 7x³.
Question 2. Which of the following is a linear polynomial?
a) 5x + 3
b) x² + 4x + 5
c) 3x³ + x
d) 7
Answer:
a) 5x + 3 — A linear polynomial has a degree of 1, as seen in 5x + 3.
Question 3. What is the coefficient of x² in the polynomial 3x² – 2x + 5?
a) 3
b) -2
c) 5
d) 0
Answer:
a) 3 — The coefficient of x² is the number multiplying x², which is 3 in this case.
Question 4. Which of the following expressions is not a polynomial?
a) 4x² + 3x + 5
b) x³ – √2x + 1
c) x⁻² + x + 7
d) 5x⁴ + 2x² + 8
Answer:
c) x⁻² + x + 7 — A polynomial cannot have negative or fractional exponents, making x⁻² + x + 7 not a polynomial.
Question 5. What is the value of the polynomial 2x² – 3x + 1 at x = 2?
a) 3
b) 5
c) 7
d) 9
Answer:
c) 7 — Substitute x = 2: 2(2²) – 3(2) + 1 = 8 – 6 + 1 = 7.
Question 6. Which of the following is a cubic polynomial?
a) x² + 2x + 1
b) x³ – x² + 2
c) 4x + 7
d) 3x⁴ + x² + 5
Answer:
b) x³ – x² + 2 — A cubic polynomial has a degree of 3, as seen in x³ – x² + 2.
Question 7. If x + 2 is a factor of the polynomial p(x) = x² + 3x + k, what is the value of k?
a) -6
b) 6
c) -2
d) 2
Answer:
a) -6 — Using the factor theorem, substitute x = -2: (-2)² + 3(-2) + k = 0 → 4 – 6 + k = 0 → k = -6.
Question 8. Which of the following statements is true for the zero polynomial?
a) Its degree is zero.
b) Its degree is undefined.
c) It has no terms.
d) It has one zero.
Answer:
b) Its degree is undefined — The degree of the zero polynomial is not defined.
Question 9. How many zeroes does a quadratic polynomial have at most?
a) 1
b) 2
c) 3
d) 0
Answer:
b) 2 — A quadratic polynomial has at most 2 zeroes, as its degree is 2.
Question 10. Which of the following represents the expanded form of (x + y)²?
a) x² + y²
b) x² + 2xy + y²
c) x² – 2xy + y²
d) x² + 4xy + y²
Answer:
b) x² + 2xy + y² — Using the identity (x + y)² = x² + 2xy + y².
Question 11. If p(x) = x³ – 4x² + 5x – 2, what is the value of p(1)?
a) 0
b) 2
c) -2
d) 3
Answer:
a) 0 — Substitute x = 1: (1)³ – 4(1)² + 5(1) – 2 = 1 – 4 + 5 – 2 = 0.
Question 12. What is the degree of the polynomial p(x) = 4x⁵ – 3x³ + 2?
a) 2
b) 3
c) 4
d) 5
Answer:
d) 5 — The highest power of x in the polynomial is 5, so the degree is 5.
Question 13. If p(x) = x² – 3x + 2, what are its zeroes?
a) 1, 2
b) -1, -2
c) 1, -2
d) -1, 2
Answer:
a) 1, 2 — Factorize: x² – 3x + 2 = (x – 1)(x – 2). The zeroes are x = 1 and x = 2.
Question 14. Which of the following represents a quadratic polynomial?
a) x³ + x² + 1
b) x² + 3x + 5
c) x + 7
d) 4
Answer:
b) x² + 3x + 5 — A quadratic polynomial has degree 2, as seen in x² + 3x + 5.
Question 15. What is the factorization of x² – 5x + 6?
a) (x – 2)(x – 3)
b) (x + 2)(x + 3)
c) (x + 1)(x – 6)
d) (x – 1)(x – 6)
Answer:
a) (x – 2)(x – 3) — Solve: Find two numbers whose product is 6 and sum is -5, i.e., -2 and -3.
Question 16. If p(x) = 2x³ – 3x² + x – 5, what is the coefficient of x?
a) 2
b) -3
c) 1
d) -5
Answer:
c) 1 — The coefficient of x in the polynomial is 1.
Question 17. Which of the following is a binomial?
a) 3x² + 2x + 1
b) x² – 1
c) x³
d) 5
Answer:
b) x² – 1 — A binomial has exactly two terms, as seen in x² – 1.
Question 18. If (x + 3) is a factor of p(x) = x² + 5x + k, what is the value of k?
a) 6
b) -6
c) 8
d) -8
Answer:
b) -6 — Using the factor theorem, substitute x = -3: (-3)² + 5(-3) + k = 0 → 9 – 15 + k = 0 → k = -6.
Question 19. Which of the following is a monomial?
a) x³ + 5
b) 3x²
c) x² + x + 1
d) 2x + 7
Answer:
b) 3x² — A monomial has exactly one term, as seen in 3x².
Question 20. Which of the following is the expanded form of (x – y)²?
a) x² – y²
b) x² – 2xy + y²
c) x² + 2xy + y²
d) x² + y²
Answer:
b) x² – 2xy + y² — Using the identity (x – y)² = x² – 2xy + y².
Question 21. If p(x) = x³ – 3x² + 4x – 12, which of the following is a factor?
a) x – 3
b) x + 3
c) x – 4
d) x + 4
Answer:
a) x – 3 — Using the factor theorem, p(3) = 3³ – 3(3²) + 4(3) – 12 = 0, so x – 3 is a factor.
Question 22. What is the value of the polynomial p(x) = x² – x + 2 at x = -1?
a) 4
b) 2
c) 0
d) 1
Answer:
b) 2 — Substitute x = -1: (-1)² – (-1) + 2 = 1 + 1 + 2 = 2.
Question 23. Which of the following polynomials has degree 4?
a) x² + 5x – 7
b) 3x⁴ – x² + 7
c) x³ – 4x² + 6
d) x + 9
Answer:
b) 3x⁴ – x² + 7 — The highest power of x in the polynomial is 4.
Question 24. Which of the following is an example of a trinomial?
a) x + 3
b) x² + 2x + 1
c) 5x³
d) x + 7y
Answer:
b) x² + 2x + 1 — A trinomial has exactly three terms, as seen in x² + 2x + 1.
Question 25. What is the expanded form of (x + y + z)²?
a) x² + y² + z² + 2xy + 2yz + 2zx
b) x² + y² + z² + xy + yz + zx
c) x² + y² + z² + 3xy + 3yz + 3zx
d) x² + y² + z²
Answer:
a) x² + y² + z² + 2xy + 2yz + 2zx — Using the identity (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx.
Question 26. If x³ + y³ = (x + y)(x² – xy + y²), what is the value of x³ + y³ when x = 2 and y = 1?
a) 9
b) 12
c) 8
d) 6
Answer:
b) 12 — Using the identity, (2 + 1)((2)² – 2(1) + (1)²) = 3(4 – 2 + 1) = 3 × 4 = 12.
Question 27. What is the factorization of x³ – y³?
a) (x – y)(x² – xy + y²)
b) (x – y)(x² + xy + y²)
c) (x + y)(x² – xy + y²)
d) (x + y)(x² + xy + y²)
Answer:
a) (x – y)(x² – xy + y²) — Using the identity x³ – y³ = (x – y)(x² – xy + y²).
Question 28. How many terms does the polynomial 3x⁴ – 5x³ + x² – 2x + 6 have?
a) 3
b) 4
c) 5
d) 6
Answer:
c) 5 — The polynomial has five distinct terms: 3x⁴, -5x³, x², -2x, and 6.
Question 29. Which of the following is not a correct algebraic identity?
a) (x + y)² = x² + 2xy + y²
b) (x – y)² = x² – 2xy + y²
c) x² – y² = (x + y)(x – y)
d) x³ + y³ = (x – y)(x² – xy + y²)
Answer:
d) x³ + y³ = (x – y)(x² – xy + y²) — This identity is incorrect; it should be x³ + y³ = (x + y)(x² – xy + y²).
Question 30. What is the zero of the polynomial p(x) = x + 7?
a) 0
b) -7
c) 7
d) 1
Answer:
b) -7 — A zero of p(x) is a value of x for which p(x) = 0. Solve x + 7 = 0 → x = -7.
