Question

The H.C.F and L.C.M of two polynomials $(x+5),(x^2+4x+16)$ respectively. If one of the polynomial is $x^2+9x+20$. Find the other.

• A. $x+5$
• B. $x+4$
• C. $x-4$
• D. $(x+4{)}^2$

Answer 1

The correct option is B $x+4$

Given:
H.C.F $=(x+5)$
L.C.M $=x^2+4x+16$
$f\left(x\right)=$ $x^2+9x+20$
$g\left(x\right)=?$
Factor of $x^2+4x+16=(x+4{)}^2$
Factor of $x^2+9x+20=(x+5)(x+4)$
Using the formula,
$f\left(x\right)\times g\left(x\right)=H.C.F\times L.C.M$
$g\left(x\right)=\frac{(x+5)(x+4{)}^2}{(x+5)(x+4)}$
$=(x+4)$
Therefore, the other polynomial is $x+4$.