by 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
- = – 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 –
- 3x⁵ + 81x²y³
- 216x³ + 343y³
- 27x² – 108
Solution –
Q- (4) Find the zeroes of the following
- p(x) = 3x – 5
- p(x) = kx
- p(x) = ax + b
Solution –
Q (5) Expand the following by using correct identities –
- (3x + y – z)²
- (3a – 7b)²
- (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 –
- 2x² – 7x – 15
- 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
