# How do you factor p^2 - 8p + 12?

May 25, 2015

Notice that $8 = 6 + 2$ and $12 = 6 \times 2$, so

${p}^{2} - 8 p + 12$

$= {p}^{2} - \left(6 + 2\right) p + \left(6 \times 2\right)$

$= \left(p - 6\right) \left(p - 2\right)$

In general form:

$\left(p - a\right) \left(p - b\right) = {p}^{2} - \left(a + b\right) p + \left(a \times b\right)$