# How do you factor 3x^3 - 2[ x - ( 3 - 2x ) ] = 3 ( x - 2 )^2?

Jan 27, 2018

The factored form is $3 \left({x}^{2} + 2\right) \left(x - 1\right) = 0$.

#### Explanation:

$3 {x}^{3} - 2 \left[\textcolor{b l u e}{x - \left(3 - 2 x\right)}\right] = 3 \textcolor{red}{{\left(x - 2\right)}^{2}}$

$3 {x}^{3} - 2 \left[\textcolor{b l u e}{x - 3 + 2 x}\right] = 3 \textcolor{red}{\left({x}^{2} - 4 x + 4\right)}$

$3 {x}^{3} - 2 \left[\textcolor{b l u e}{3 x - 3}\right] = \textcolor{red}{3 {x}^{2} - 12 x + 12}$

$3 {x}^{3} - \textcolor{b l u e}{6 x + 6} = \textcolor{red}{3 {x}^{2} - 12 x + 12}$

$3 {x}^{3} - 3 {x}^{2} + 6 x - 6 = 0$

$3 {x}^{2} \left(x - 1\right) + 6 \left(x - 1\right) = 0$

$\left(3 {x}^{2} + 6\right) \left(x - 1\right) = 0$

$3 \left({x}^{2} + 2\right) \left(x - 1\right) = 0$