# How do you factor p^2 + 12p + 32?

Jun 4, 2015

If $\left({p}^{2} + 12 p + 32\right)$
$\textcolor{w h i t e}{\text{XXXX}}$has factors $\left(p + a\right) \left(p + b\right)$

then we need to find values $a$ and $b$ such that
$\textcolor{w h i t e}{\text{XXXX}}$$a + b = 12$ and
$\textcolor{w h i t e}{\text{XXXX}}$$a \times b = 32$

With a bit of consideration of the possible factors of $32$
we can come up with $\left(4 , 8\right)$

So
$\textcolor{w h i t e}{\text{XXXX}}$${p}^{2} + 12 p + 32 = \left(p + 4\right) \left(p + 8\right)$