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: Which of the following is NOT a polynomial?
a) 4x² – 3x + 7
b) y² + 2
c) 3/x + 2
d) 5t – 7
Answer:
c) 3/x + 2
Question 2: What is the degree of the polynomial 7x³ – 4x² + 2x – 9?
a) 1
b) 2
c) 3
d) 4
Answer:
c) 3
Question 3: A polynomial with only one term is called a ___.
a) Binomial
b) Trinomial
c) Monomial
d) Constant
Answer:
c) Monomial
Question 4: Which of the following is a quadratic polynomial?
a) 2x + 1
b) 5 – y²
c) 3x³ – 1
d) 7
Answer:
b) 5 – y²
Question 5: The zero of the polynomial p(x) = 2x + 1 is:
a) 1/2
b) –1/2
c) 2
d) –2
Answer:
b) –1/2
Question 6: How many zeroes does a linear polynomial have?
a) None
b) Exactly one
c) At least two
d) Infinitely many
Answer:
b) Exactly one
Question 7: Which of these polynomials has 0 as a zero?
a) x + 2
b) 3x² – 1
c) x² – 2x
d) 2x + 5
Answer:
c) x² – 2x
Question 8: The zero polynomial has how many zeroes?
a) None
b) One
c) Infinitely many
d) Two
Answer:
c) Infinitely many
Question 9: If p(x) = x – 3, then its zero is:
a) 3
b) –3
c) 0
d) 1
Answer:
a) 3
Question 10: What is the value of k if x – 1 is a factor of 4x³ + 3x² – 4x + k?
a) 0
b) –3
c) 3
d) 1
Answer:
b) –3
Question 11: Which of these polynomials is divisible by x + 2?
a) x³ + 3x² + 5x + 6
b) x² + 1
c) 3x + 1
d) x³ – 2x² – x + 5
Answer:
a) x³ + 3x² + 5x + 6
Question 12: The Factor Theorem states that (x – a) is a factor of p(x) if:
a) p(a) = 1
b) p(a) = a
c) p(a) = 0
d) a = 0
Answer:
c) p(a) = 0
Question 13: Which of the following is a cubic polynomial?
a) x² + 3
b) x³ – 4x
c) 5x – 7
d) 2
Answer:
b) x³ – 4x
Question 14: Factorise y² – 5y + 6. Which is correct?
a) (y – 2)(y – 3)
b) (y + 2)(y – 3)
c) (y – 1)(y – 6)
d) (y + 1)(y + 6)
Answer:
a) (y – 2)(y – 3)
Question 15: The degree of a non-zero constant polynomial is:
a) 0
b) 1
c) Undefined
d) Infinite
Answer:
a) 0
Question 16: Which polynomial has both 2 and 0 as zeroes?
a) x² – 2x
b) x² + 2
c) 2x + 1
d) x³ – 2
Answer:
a) x² – 2x
Question 17: If p(x) = x³ – 23x² + 142x – 120, then one of its factors is:
a) x + 2
b) x – 12
c) x – 1
d) x + 10
Answer:
c) x – 1
Question 18: Which identity is correct for (x + y)³?
a) x³ + y³
b) x³ + y³ + 3xy(x + y)
c) x³ – y³ + 3xy(x – y)
d) x² + y²
Answer:
b) x³ + y³ + 3xy(x + y)
Question 19: Expand (x – y)³.
a) x³ – y³ – 3xy(x – y)
b) x³ + y³ – 3xy(x – y)
c) x³ – y³ + 3xy(x + y)
d) x³ + y³ + 3xy(x – y)
Answer:
a) x³ – y³ – 3xy(x – y)
Question 20: The factorisation of x² – y² is:
a) (x – y)²
b) (x + y)²
c) (x + y)(x – y)
d) (x – y)(x – y)
Answer:
c) (x + y)(x – y)
Question 21: The degree of the zero polynomial is:
a) 0
b) 1
c) Undefined
d) 2
Answer:
c) Undefined
Question 22: Which of the following is a trinomial?
a) x + 1
b) x² – x + 1
c) 2x²
d) 5
Answer:
b) x² – x + 1
Question 23: Using identity (x + y + z)², the expansion of (x + y + z)² is:
a) x² + y² + z²
b) x² + y² + z² + 2xy + 2yz + 2zx
c) x² + y² + z² – 2xy – 2yz – 2zx
d) (x + y + z)(x – y – z)
Answer:
b) x² + y² + z² + 2xy + 2yz + 2zx
Question 24: Factorise 6x² + 17x + 5. Which is correct?
a) (3x + 1)(2x + 5)
b) (3x + 5)(2x + 1)
c) (x + 5)(6x + 1)
d) (2x + 3)(3x + 5)
Answer:
a) (3x + 1)(2x + 5)
Question 25: The value of (104)³ is:
a) 1124864
b) 1048576
c) 1040000
d) 1000000
Answer:
a) 1124864
Question 26: Which polynomial has –2 as a zero?
a) x + 2
b) x – 2
c) x² + 4
d) 3x – 1
Answer:
a) x + 2
Question 27: If p(x) = 2x³ + x² – 2x – 1, then p(–1) =
a) 0
b) –2
c) 1
d) –1
Answer:
a) 0
Question 28: Which is a factor of y² – 5y + 6?
a) y + 2
b) y – 2
c) y + 3
d) y – 6
Answer:
b) y – 2
Question 29: If (x – 1) is a factor of x² + x + k, then k =
a) 1
b) –1
c) 2
d) –2
Answer:
b) –1
Question 30: Which identity is true for 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:
b) (x + y)(x² – xy + y²)
Question 31: The expansion of (x + y – z)² is:
a) x² + y² + z² + 2xy – 2xz – 2yz
b) x² + y² + z² – 2xy + 2xz – 2yz
c) x² + y² + z² + 2xy + 2xz – 2yz
d) x² + y² + z² – 2xy – 2xz + 2yz
Answer:
a) x² + y² + z² + 2xy – 2xz – 2yz
Question 32: Factorise 8x³ + 27y³.
a) (2x + 3y)(4x² – 6xy + 9y²)
b) (2x – 3y)(4x² + 6xy + 9y²)
c) (2x + 3y)(4x² + 6xy + 9y²)
d) (2x – 3y)(4x² – 6xy + 9y²)
Answer:
a) (2x + 3y)(4x² – 6xy + 9y²)
Question 33: If x + y + z = 0, then x³ + y³ + z³ =
a) 0
b) 3xyz
c) x² + y² + z²
d) –3xyz
Answer:
b) 3xyz
Question 34: Which identity is correct for x³ + y³ + z³ – 3xyz?
a) (x + y + z)(x² + y² + z² – xy – yz – zx)
b) (x – y – z)(x² + y² + z²)
c) (x + y + z)(x² + y² + z² + xy + yz + zx)
d) (x – y – z)(x² – y² – z²)
Answer:
a) (x + y + z)(x² + y² + z² – xy – yz – zx)
Question 35: Factorise x³ – 3x² – 9x – 5.
a) (x – 5)(x² + 2x + 1)
b) (x – 1)(x² – 2x – 5)
c) (x – 5)(x² + 3x – 1)
d) (x – 1)(x² – 2x – 5)
Answer:
b) (x – 1)(x² – 2x – 5)
Fill in the blanks on Polynomials for Class 9 Maths
1. A polynomial in one variable x of degree n is of the form ___.
Answer:
anxⁿ + an–1xⁿ⁻¹ + … + a1x + a0, where an ≠ 0
2. The degree of the polynomial 7x³ – 4x² + x + 9 is ___.
Answer:
3
3. A polynomial with only one term is called a ___.
Answer:
Monomial
4. A polynomial of degree two is called a ___ polynomial.
Answer:
Quadratic
5. The degree of the zero polynomial is ___.
Answer:
Not defined
6. The coefficient of x³ in –x³ + 4x² + 7x – 2 is ___.
Answer:
–1
7. The zero of the polynomial p(x) = 2x + 1 is ___.
Answer:
–1/2
8. Every linear polynomial in one variable has exactly ___ zero.
Answer:
one
9. A non-zero constant polynomial has ___ zeroes.
Answer:
no
10. If p(x) = x² – 2x, then its zeroes are ___ and ___.
Answer:
0, 2
11. If x – 1 is a factor of 4x³ + 3x² – 4x + k, then the value of k is ___.
Answer:
–3
12. The Factor Theorem states that (x – a) is a factor of p(x) if and only if ___.
Answer:
p(a) = 0
13. The factorisation of y² – 5y + 6 is ___.
Answer:
(y – 2)(y – 3)
14. The cubic polynomial x³ – 23x² + 142x – 120 can be factorised as ___.
Answer:
(x – 1)(x – 10)(x – 12)
15. The expansion of (x + y)² is ___.
Answer:
x² + 2xy + y²
16. The expansion of (x – y)³ is ___.
Answer:
x³ – 3x²y + 3xy² – y³
17. The identity (x + y + z)² expands to ___.
Answer:
x² + y² + z² + 2xy + 2yz + 2zx
18. According to the identity, x³ + y³ = ___.
Answer:
(x + y)(x² – xy + y²)
19. The identity x³ + y³ + z³ – 3xyz can be factorised as ___.
Answer:
(x + y + z)(x² + y² + z² – xy – yz – zx)
20. If x + y + z = 0, then x³ + y³ + z³ = ___.
Answer:
3xyz
