CBSE Class 9 Mathematics Polynomials Assignment Set 01

Question. Given P = Product of x²y and x/y and Q = Quotient obtained when x² is d ivided by D. If P = Q what is the value of D?
(A) 0
(B) 1
(C) x
(D) 1/X
Answer : D

Question. Which of the following is one of the factors of a³ + 8b³ - 64c³ + 24abc?
(A) a + 2b - 4c
(B) a - 2b + 4c
(C) a + 2b + 4c
(D) a - 2b - 4c
Answer : A

Question. Factorise: a⁴ + 4
(A) (a² + 2a - 2)(a² + 2a + 2)
(B) (a² - 2a - 2)(a² + 2a - 2)
(C) (a² + 2a - 2)(a² - 2a + 2)
(D) (a² + 2a + 2)(a² - 2a + 2)
Answer : D

Question. Factorise a^2x - b^2x.
(A) (a^x + b^x) (a^x - b^x)
(B) (a^x - b^x)²
(C) (a^x + b^x) (a² - b²)
(D) (a^x- b^x) (a² + b²)
Answer : A

Question. If p = (2 - a), what is a³ + 6ap + p³ - 8?
(A) 1
(B) 0
(C) 2
(D) 3
Answer : B

Question. Find the value of (x - a)³ + (x - b)³ + (x - c)³ - 3(x - a) (x- b) (x - c) when a + b + c = 3x.
(A) 3
(B) 2
(C) 1
(D) 0
Answer : D

Question. Find the zero of t he polynomial f(x) = qx, q≠O.
(A) 1
(B) b
(C) 0
(D) - 1
Answer : C

Question. If x - 1 is a factor of f(x) = x³ - 6x² + 11 x - 6, which of the following is true?
(A) f(-x) = 0
(B) f(-1) = 0
(C) f(x) = 0
(D) f(1) = 0
Answer : D

Question. If y - 2 and y - 1/2 are the factors of py² + 5y + r, which of the following holds good?
(A) p > r
(B) p = r
(C) p < r
(D) Both (A) and (C)
Answer : B

Question. If the factors of a² + b² + 2(ab + bc + ca) are (a + b + m) and (a + b + nc), find the value of m + n.
(A) 0
(B) 2
(C) 4
(D) 6
Answer : B

Question. Which of the following is a trinomial in p?
(A) x² + 5
(B) p³ + p² + √2
(C) √p (1 + √2P) 
(D) y +1/y + 1/2
Answer : B

Question. Identify one of the factors of x² + 1/x² + 2 - 2x - 2/x from the following.
(A) X - 1/x
(B) x + 1/x - 1
(C) X + 1/x
(D) x² + 1/x²
Answer : C

Question. Write the degree of the polynomial 0.
(A) 1
(B) 0
(C) N
(D) Not defined
Answer : D

Question. If the quot ient is 3x² - 2x + 1, remainder is 2x - 5 and divisor is x + 2, what is the dividend?
(A) 3x³ - 4x² + x - 3
(B) 3x³ - 4x² - x + 3
(C) 3x³ + 4x² - x + 3
(D) 3x³ + 4x² - x - 3
Answer : D

Question. What are the factors of 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)
Answer : C

Question. lf (x² + 3x + 5) (x² - 3x + 5) = m² - n², find m.
(A) x² - 3x
(B) 3x + 5
(C) x² + 5
(D) x² - 5
Answer : C

Question. If x/y + y/x = - 1 (x,y ≠ 0), what is the value of x³ - y³?
(A) 1
(B) - 1
(C) 1/2
(D) 0
Answer : D

Question. Express x - 8xy³ as product of factors.
(A) x(1 - 2y) (1 + 2y + 4y²)
(B) x(1 + 2y) (1 + 2y + 4y²)
(C) x(1 - 2y) (1 - 2y + 4y²)
(D) x(1 + 2y) (1 - 2y + 4y²)
Answer : A

Question. Factorise: ab (a + b)² - 3ab(a + b)
(A) (a + b) (a - b)ab
(B) (a + b - 5) (2a +b) (a - b)
(C) ab(a + b)(a + b - 3)
(D) ab(2a - b) (2a + b- 6)
Answer : C

Question. Factorise: x² - z² + y² - p² + 2pz - 2xy
(A) (x - y - p - z) (x - y - p + z)
(B) (x - y + p - z) (x- y- p + z)
(C) (x + y + p - z) (x + y + p + z)
(D) (x + y - p + z) (x - y - p + z)
Answer : B

Question. Which of the following polynomials has - 5 as a zero?
(A) (p - 5)
(B) x² - 25
(C) p² - 5p
(D) x² + 5
Answer : B

Question. If x^1/3 + y^1/3 + z^1/3 = 0 ,which of t he following is true?
(A) x³ + y³ + z³ = 0
(B) x + y + z = 27xyz
(C) (x + y + z)³ = 27xyz
(D) x³ + y³ + z³ = 27xyz
Answer : C

Question. Find the value of 'a' if the polynomials 2x³ + ax² + 3x - 5 and x³ + x² - 4x - a leave the same remainder when divided by X - 1 .
(A) a = 1
(B) a = - 1
(C) a = 2
(D) a = - 2
Answer : B

Question. Identify one of the factors of x¹² - y¹²
(A) (x² - xy + y²)
(B) (x⁴ + x²y² + y⁴)
(C) (x² + xy- y²)
(D) (x⁴ - xy + y⁴)
Answer : A

Question. If x + y + z = 0, what is the value of x³ + y³ + z³?
(A) xyz
(B) 2xyz
(C) 3xyz
(D) 0
Answer : C

Question. If a + b + c = 0, evaluate a²/bc + b²/ca + c²/ab
(A) 1
(B) 2
(C) 3
(D) 4
Answer : C

Question. If (x - 2) is one factor of x² + ax - 6 = 0 and x² - 9x + b = 0, find a + b.
(A) 15
(B) 13
(C) 11
(D) 10
Answer : A

Question. Reso lve into factors: 6x³ - 24xy² - 3x²y + 12y³
(A) 3(2x- y) (x - 2y) (x + y)
(B) 3(2x - y) (x + y) (x + 2y)
(C) 3(2x- y) (x + 2y) (x - 2y)
(D) 3(2x + y) (x - y) (x + 2y)
Answer : A

Question. Identify the degree of the polynomial 4 - x² - x³ + 5x⁷/3
(A) 2
(B) 7
(C) 0
(A) 3
Answer : B

Question. If x + 1/x = a+ b and x - 1/x = a - b , which of the following is true?
(A) ab = 1
(B) a = b
(C) ab = 2
(D) a + b = 0
Answer : A

Question. Find the value of 2^1/4. 4^1/8. 16^1/16. 256^1/32.
(A) 1
(B) 2
(C) 4
(D) 8
Answer : B

Question. What is the value of 0.96 x 0.96 x 0.96 + 0.04 x 0.04 x 0.04/0.96 x 0.96 - 0.96 X 0.04 + 0.04 x 0.04 ?
(A) 0
(B) 2
(C) 1
(D) Not defined
Answer : C

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