Question

How do you factor the expression $x^2-7x+12$?

Answer 1

Factorize the given expression using the common factor method

The given expression is $x^2-7x+12$.

The given expression can be factorized as follows,

$x^2-7x+12=x^2-3x-4x+12$ $\left[\because \left(-3\right)\times \left(-4\right)=+12,-3-4=-7\right]$

$\Rightarrow x^2-7x+12=\left(x^2-3x\right)-\left(4x-12\right)$

$\Rightarrow x^2-7x+12=x\left(x-3\right)-4\left(x-3\right)$ $\mathrm{[}\mathrm{\because }\mathrm{}\mathrm{ab}\mathrm{-}\mathrm{ac}\mathrm{=}\mathrm{a}\left(b-c\right)\mathrm{]}$

$\Rightarrow x^2-7x+12=\left(x-3\right)\left(x-4\right)$

Hence, the factors of $x^2-7x+12$ obtained by using the common factor method is $\left(x-3\right)\left(x-4\right)$.