The HCF of two polynomials $p(x)$ and $q(x)$ is $2x (x+2)$ and LCM is $24x (x+2)^2 (x-2)$. If $p(x) = 8x^3 + 32x^2+32x$, then what is $q(x)$ equal to?
Solution
If p(x) and q(x) are two polynomials, then
p(x).q(x) = [HCF of p(x) and q(x)][LCm of p(x) and q(x)]
$(8x^3 +32x^2 + 32x) (q(x)) = [2x (x + 1)][24x (x + 2)^2 (x-2)]$
$q(x) = \dfrac{648x^2 (x + 1)(x + 2)^2 (x-2)}{8x(x^2 + 4x + 4)}$
$q(x) = 6x^3 - 24x$