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)}`