# How do I factor using the zero factor property?

Jan 9, 2016

The zero factor property states that if $a b = 0$, then either $a = 0$ or $b = 0$.

Example: find the roots of ${x}^{2} - x - 6$.

${x}^{2} - x - 6 = 0$

$\left(x - 3\right) \left(x + 2\right) = 0$

Now, the zero factor property can be applied, since two thing are being multiplied and equal zero.

We know that either

$x - 3 = 0 \textcolor{w h i t e}{s s s s}$ or $\textcolor{w h i t e}{s s s s} x + 2 = 0$

Solve both to find that $x = 3$ or $x = - 2$.