Question

How do you factorise the expression $x^2-x-6$?

Answer 1

Factorize the given expression using the common factor method

The given expression is $x^2-x-6$.

The given expression can be factorized as follows,

$x^2-x-6=x^2-3x+2x-6$ $\left[\because \left(-3\right)\times \left(2\right)=-6,-3+2=-1\right]$

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

$\Rightarrow x^2-x-6=x\left(x-3\right)+2\left(x-3\right)$ $\mathrm{[}\mathrm{\because }\mathrm{}\mathrm{ab}\mathrm{-}\mathrm{ac}\mathrm{=}\mathrm{a}\left(b-c\right)\mathrm{]}$

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

Hence, the factors of $x^2-x-6$ obtained by using the common factor method is $\left(x-3\right)\left(x+2\right)$.