Question

What's one of the factors of x² - x – 6 ?

Answer 1

$x^2-x-6=x^2+2x-3x-6=x(x+2)-3(x+2)\\\\=\boxed{(x+2)(x-3)}$

The factors are: (x+2) and (x-3).

$x^2-x-6=x^2+\underbrace{2x-3x}_{=-x}-6\\\\=\underbrace{x\cdot\boxed{x}}_{=x^2}+\underbrace{2\cdot\boxed{x}}_{=2x}+\underbrace{\fbox{-3}\cdot x}_{=-3x}+\underbrace{\fbox{-3}\cdot2}_{=-6}=\boxed{x}(x+2)+\fbox{-3}(x+2)\\\\=(x+2)(x+(-3))=\boxed{(x+2)(x-3)}$