# How do you factor a perfect square trinomial 9x^2 − 12x + 4?

Jul 7, 2015

$9 {x}^{2} - 12 x + 4 = {\left(3 x - 2\right)}^{2}$

#### Explanation:

If $A {x}^{2} + B x + C = {\left(a x + c\right)}^{2}$ is a perfect square trinomial
then for some set $\left\{a , c\right\}$
$\textcolor{w h i t e}{\text{XXXX}}$$A = {a}^{2}$
$\textcolor{w h i t e}{\text{XXXX}}$$C = {c}^{2}$
and
$\textcolor{w h i t e}{\text{XXXX}}$$B = 2 a c$

Given that $9 {x}^{2} - 12 x + 4$ is a perfect square trinomial
$\textcolor{w h i t e}{\text{XXXX}}$$A = 9 {x}^{2} \rightarrow a = 3 x$
$\textcolor{w h i t e}{\text{XXXX}}$$C = 4 \rightarrow c = \pm 2$

Since $B = - 12 x = 2 a c = 2 \left(3 x\right) c$
$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow c = - 2$