December 2, 2022

# Class 9 maths polynomials Chapter 2 extra questions

Class 9 maths chapter 2 Polynomials subjective questions for term 2 exams.

Subjective questions

## Class 9 – Maths Chapter – 2 Polynomials

Quiz -1 (2 Mark Questions)

Q- (1) Show how (x + a) is a factor of xⁿ + aⁿ for any odd positive integer n.

Solution : Here f(x) = xⁿ + aⁿ

And g(x) = x + a, If (x + a) is the factor of xⁿ + aⁿ

Then f(-a) = 0 as g(x) = 0 so x + a = 0

x = -a

So f(-a) = (-a)ⁿ + aⁿ = 0 (since n is a odd positive integer)

Hence (x + a) is a factor of xⁿ + aⁿ.

Q- (2) If (x + 1) and (x – 1) both are the factors of ax³ + x² – 2x + b, find the value of a and b.

Solution – Here f(x) = ax³ + x² – 2x + b

And x + 1 is the factor so x = -1

So f(-1) = a(-1)³ + (-1)² – 2(-1) + b

1. = – a + b + 3

a – b = 3 ……………………. Eq(1)

And x – 1 is a factor so x = 1

So f(1) = a(1)³ + (1)² – 2(1) + b

0 = a + 1 – 2 + b

a + b = 1 ………………………. Eq(2)

by eq(1) a = b + 3

and putting it in eq(2) b + 3 + b = 1

b = -1,

a = -1 + 3 = 2

Q- (3) Factorize the following –

1. 3x⁵ + 81x²y³
2. 216x³ + 343y³
3. 27x² – 108

Solution –

Q- (4) Find the zeroes of the following

1. p(x) = 3x – 5
2. p(x) = kx
3. p(x) = ax + b

Solution –

Q (5) Expand the following by using correct identities –

1. (3x + y – z)²
2. (3a – 7b)²
3. (1 – a)(1 – b)

Q-(6)Factorize : (i) (5x + 2/3)² – (2x – 1/3)²

(ii) (2x – 5y)³ – (2x + 5y)³

Q- (7) Factorize :

(i) 3x² + 4y² + 25z² – 4√3xy – 20 yz + 10√3 zx

(ii) x⁸ – y⁸ (iii) x⁶ – y⁶

Q- (8) Without actually doing division , prove that 2x⁴ + x³ – 14x² – 19x – 6 is exactly divisible by x² + 3x + 2.

Q- (9) If both (x – 2) and (x – ½) are the factors of px² + 5x + r, show that p = r.

Q- (10) Factorize –

1. 2x² – 7x – 15
2. x³ + x² – 4x – 4

Q- (11) If z² + 1/z² = 14, find the value of z³ + 1/z³.

Q- (12) If x + 1/x = 3, find the value of x⁴ + 1/x⁴.

Q- (13) If x² + 1/x² = 34, Find  x³ + 1/x³ – 9.

Q- (14) If p(x) = 10x – 4x² – 3, and q(x) = (x + 2)(x – 2). Then find the value of p(0) x q(3).

Q- (15) If p(x) = x³ – 4x + 3, evaluate p(2) – p(-1) + p(1/2).

Q- (16) Find the value of k if (x – 3) is a factor of x² – kx – 2.

Q- (17) Find the product (5a – 3b)(25a² + 15ab + 9b²).

Q- (18) t² – 1 is a factor of at³ + t² – 2t + b, find the values of a and b.

Q- (19) Factorize – x² + 1/x² + 1

Q- (20) Factorize –   (a)  a⁷ – ab⁶             (b) 16a⁴ + 54a

Q- (21) If x = -1/2 is a zero of the polynomial, p(x) = 8x³ – k, find the value of k.

Q- (22) Find the factors by factorization method –

(a) x² – x – 6

(b) 16x² + 8x + 1

Q- (23) Evaluate – (a)  101 x 99

(b) 998³