Question

The HCF of two polynomials P(x) and q(x) is 2x(x + 2) and L.C.M is24x(x + 2)

2(x − 2) .If

P(x) = 8x3 + 32x2 + 32x , then q(x) is

A) 4x3 − 6x
B) 6x3 − 24x
C) 12x3 + 24x
D) 12x3 − 24x​

Answer 1

Given, HCF of p(x) and q(x) is 2x(x + 2) and

LCM = 24x(x + 2)2(x - 2), p(x) = 8x +

32x2 + 32

HCF X LCM

q(x) =

;P(x) = 8x(x + 2)2

p(x)

2x(x + 2) × 24x(x + 2)(x - 2)

8x(x + 2)2

6x(x + 2)(x - 2)

6x(x² – 4)

= 6x3 – 24x

Hope this helps....