Question

Find the LCM of : $-x^2-x+6,-x^2+x+2$

Answer 1

We know that $LCM$ is the least common multiple.

Factorise $-x^2-x+6$ as follows:

$-x^2-x+6=-(x^2+x-6)=-(x^2+3x-2x-6)=-\left[x\right(x+3)-2(x+3\left)\right]=-(x-2)(x+3)=(2-x)(x+3)$

Now, factorise $-x^2+x+2$ as follows:

$-x^2+x+2=-(x^2-x-2)=-(x^2-2x+x-2)=-\left[x\right(x-2)+1(x-2\left)\right]=-(x+1)(x-2)=(2-x)(x+1)$

Therefore, the least common multiple between the polynomials $-x^2-x+6$and $-x^2+x+2$ is:

$LCM=(2-x)(x+3)(x+1)$

Hence, the $LCM$ is $(2-x)(x+3)(x+1)$.