Question

Find the L.C.M and H.C.F of two polynomials, $p\left(x\right)$ and $q\left(x\right)$ are $12(x^2-4)$ and $(x-1)(x+3)$ respectively. If $q\left(x\right)=4(x+2)(x+3)$, find $p\left(x\right)$.

• A. $3(x-2)(x-2)$
• B. $3(x-1{)}^2(x-2)$
• C. $3(x-1)(x-2)$
• D. $(x-1)(x-2)$

Answer 1

The correct option is C $3(x-1)(x-2)$

Given:
$p\left(x\right)=?$
$q\left(x\right)=4(x+2)(x+3)$
L.C.M $=12(x^2-4)=12(x+2)(x-2)$
So, H.C.F $=$ $(x-1)(x+3)$
Using the formula,
$p\left(x\right)\times q\left(x\right)=$ H.C.F $\times$ L.C.M
$p\left(x\right)=\frac{12(x+2)(x-2)(x-1)(x+3)}{4(x+2)(x+3)}$
$=3(x-1)(x-2)$
Therefore, $p\left(x\right)$ is $3(x-1)(x-2)$.