Question

Determine the L.C.M and H.C.F of two polynomials, $p\left(x\right)$ and $q\left(x\right)$ are $(x^2-9)$ and $2(x+1{)}^2$ respectively. If $p\left(x\right)=12(x+1)(x-3)$, find $q\left(x\right)$.

• A. $\frac{(x+3)(x+1)}{6}$
• B. $\frac{(x-3)(x+1)}{6}$
• C. $\frac{(x+1)}{6}$
• D. $\frac{(x-3)(x+1)}{24}$

Answer 1

The correct option is B $\frac{(x-3)(x+1)}{6}$

Given:
$p\left(x\right)=12(x+1)(x-3)$
$q\left(x\right)=?$
L.C.M $=(x^2-9)=(x+3)(x-3)$
So, H.C.F $=$ $2(x+1{)}^2$
Using the formula,
$p\left(x\right)\times q\left(x\right)=H.C.F\times L.C.M$
$q\left(x\right)=\frac{2(x+3)(x-3)(x+1{)}^2}{12(x+1)(x-3)}$
$=\frac{(x-3)(x+1)}{6}$
Therefore, $q\left(x\right)$ is $\frac{(x-3)(x+1)}{6}$.