# How do you factor f(x)=x^2+8x+16?

Jun 27, 2018

${\left(x + 4\right)}^{2}$

#### Explanation:

We need a pair of numbers that add to make $8$ and multiply to make $16$:

List the factors of $16$:

$16 \mathmr{and} 1$

$\Rightarrow 16 + 1 = 17$

$8 \mathmr{and} 2$

$\Rightarrow 8 + 2 = 10$

$4 \mathmr{and} 4$

$\Rightarrow 4 + 4 = 8$

$\therefore$ we place these in brackets:

$\Rightarrow \left(x + 4\right) \left(x + 4\right)$

Which can be written as:

${\left(x + 4\right)}^{2}$