CBSE Class 9 Mathematics Polynomials Worksheet Set 02

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)
Answer : A

Question. A cubic polynomial cannot have more than ______ zeroes.
(a) 0
(b) 1
(c) 2
(d) 3
Answer : D

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

Question. Which of the following is a cubic polynomial?
(a) 2x + √3 + x⁴
(b) – x – x² – 7x³
(c) 9
(d) 2 – 3x² – 9x
Answer : B

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

Question. Factors of (42 – x – x²) are
(a) (x – 7), (x – 6)
(b) (x + 7), (x – 6)
(c) (x + 7), (6 – x)
(d) (x – 7), (x + 6)
Answer : C

Question. The value of the polynomial 5x – 4x² + 3, when x = – 1 is
(a) – 6
(b) 6
(c) 2
(d) – 2
Answer : A

Question. Degree of the polynomial p(x) = (x + 2)(x – 2) is
(a) 2
(b) 1
(c) 0
(d) 3
Answer : A

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

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

Question. The common quantity that must be added to each term of a² : b² to make it equal to a : b is
(a) ab
(b) a + b
(c) a – b
(d) a/b
Answer : A

Question. Find the value of x + y + z, if x² + y² + z² = 18 and xy + yz + zx = 9.
(a) 9
(b) 3
(c) 6
(d) 8
Answer : C

Question. Number of terms in the polynomial 4x³ + 3x² – 6x + 7 is
(a) 1
(b) 2
(c) 3
(d) 4
Answer : D

Question. Degree of polynomial 2x³ +√3x + (1/3) x⁵ − 7 is
(a) 1
(b) 3
(c) 0
(d) 5
Answer : D

Question. If f(x) = x³ – 3x² + 4x + 50, then f(–3) =
(a) –16
(b) –12
(c) –20
(d) –10
Answer : A

Question. If p(x) = x³ + 3x² – 2x + 4, then find the value of [p(2) + p(–2) – p(0)].
(a) 28
(b) 14
(c) 12
(d) 16
Answer : A

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

Question. If p(x) = x² − 2√2x +1, then p(2√2) =
(a) 0
(b) 1
(c) 4 2
(d) –1
Answer : B

Question. If a + b + c = 0, then a³ + b³ + c³ is equal to
(a) 0
(b) abc
(c) 3abc
(d) 2abc
Answer : C

Question. √2 is a polynomial of degree
(a) 2
(b) 0
(c) 1
(d) 1/2
Answer : B

Case Based MCQs

Case I : Read the following passage and answer the questions from 1 to 5.
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.

1. Coefficient of x² in the given polynomial is
(a) 2
(b) 3
(c) 4
(d) 12
Answer : C

2. Total amount invested by both, if x = 1000 is
(a) ₹ 301506
(b) ₹ 370561
(c) ₹ 4012005
(d) ₹ 490621
Answer : C

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

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

5. 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
Answer : C

Q.1 Factorize the following by splitting the middle term:

(a) 3x2 + 11x+30 (b) 22 x2 +9x+52 (c) 4x2 - 13x + 10 Q.2 Factorize the following by Factor theorem:

(a)x3+9 x2 +23x+15 (b) x3+6 x2 +11x+6

Q.3 Factorize the following by using a suitable identity:

(a) 4x2 + 12xy + 9y2 (b) 2a5 – 54 a2 (c) 22x3 + 3 3 y3 (d) x5- x (e) x6 – y6 (f) (a-b)3 + (b-c)3 +(c-a)3 (f) x8-y8 (g) 27x3-135x2 +225x -125

Q.4 Evaluate the following using a suitable identity:

(a) 9983 (b) 10.23 (c) 9.83 (d) 9982-4 (e) 9992 -1 (f) (-25)3 + 10 3 +15 3 (g) 10.2 * 9.8

Q.5 If 5 is a zero of x3 + kx2 + 2x +8 find k.

Q.6 If (x-2) is a zero of of x3 -4x2 + kx -8 find k.

Q.7 If ( x-2 ) and (x +3) are factors of x3 + ax2 +bx -30, find a and b.

Q.8 If x+y+ z = 8 and xy +yz+zx = 20 find the value of x3+y3+z3 -3xyz.

Q.9 If a+b+c = 9 and a2 +b2+c2 =35 find the value of a3+b3+c3 – 3abc.

Q.10 Find the value of 2.73 -1.63-1.13 using a suitable identity.

Q.11 Factorize the following by using a suitable identity:

(a) a3 +b3 – 8c3 + 6abc (b) (a/b)3 + (b/c)3 + (c/a)3 -3 (c) 8x3 -27y3 + 125 z3 + 90xyz

Q.12 Find the value of a3 + 8b3 if a + 2b = 10 and ab =15.

Q.13 Find the value of a3 -27b3 if a - 3b =( -6) and ab = (-10)

Q.14 Find the values of m and n if y2-1 is a factor of y4 + my3 +2y2 -3y +n.

Q.15 (x +2 ) is a factor of mx3 +nx2+x-6. It leaves the remainder 4 when divided by (x-2). Find m and n.

Q.16 The polynomials kx3 + 3x2 -3 and 2x3 – 5x +k leave the same remainder when divided by (x-4). Find k.

Q.17 Factorize : x3 + 1/x3 - 2

Q.18 If ab + bc+ ca = 10 and a2 +b2 +c2 = 44 find a3 +b3 +c3 -3abc.

Q.19 Show that x-2 is a factor p(x) = x3-12x2+ 44x-48

Q.20 Factorize x3-2x2-5x+6

Q.21 If x+p is a factor of p(x) = x5-p2x3+2x+p+1 find the value of p

Q.22 Factorize: (a) a2 + 1/a2 +2 (b) 3(x+2)2 + 17(x+2) +10 (c)4x2 – 9 y2 + 20x + 25

Prepared by: ROY MATHEW

Please click the below link to access CBSE Class 9 Mathematics Worksheet - Polynomials (1)