Question

Find the other polynomial $q\left(x\right)$, if L.C.M and H.C.F is $(x+1{)}^2$ and $(x+2{)}^2$, then $p\left(x\right)$ is $x^2+3x+2$ respectively.

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

Answer 1

The correct option is C $(x+1)(x+2)$

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