# How do you write x^2-13x+12 in factored form?

Apr 25, 2018

${x}^{2} - 13 x + 12 = \textcolor{red}{\left(x - 1\right) \left(x - 12\right)}$

#### Explanation:

Remember
color(white)("XXX")(x+color(blue)a) * (x+color(lime)b))=x^2+(color(blue)a+color(lime)b)x+color(blue)acolor(lime)b

So we are looking for two values, $\textcolor{b l u e}{a}$ and $\textcolor{\lim e}{b}$, such that
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{a} + \textcolor{\lim e}{b} = - 13$
and
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{a} \cdot \textcolor{\lim e}{b} = 12$