Question

Find the HCF $h\left(x\right)$ of the following polynomials and using HCF $h\left(x\right)$, find the LCM $m\left(x\right)$, the polynomials are $16-4x^2,x^2+x-6$

Answer 1

Let $p\left(x\right)=16-4x^2$

$=4^2-(2x{)}^2$

$=(4-2x)(4+2x)$

$=(4-2x)(4+2x)$

$\therefore p\left(x\right)=-2(x-2)(4+2x)$

And $q\left(x\right)=x^2+x-6$

$=x^2+3x-2x-6$

$=x(x+3)-2(x+3)$

$=(x+3)(x-2)$

$\therefore$ HCF $h\left(x\right)=(x-2)$

LCM $m\left(x\right)=(x-2)(-2)(4+2x)(x+3)$

$=-4(x-2)(x+2)(x+3)$

$=-4(x^2-4)(x+3)$