# How do you factor 2x^3-3x^2-2x+3?

Jul 4, 2017

$\left(2 x - 3\right) \left(x - 1\right) \left(x + 1\right)$

#### Explanation:

$2 {x}^{3} - 3 {x}^{2} - 2 x + 3$

First, start off by factoring the first two terms.

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

Next, factor out the last two terms.

${x}^{2} \left(2 x - 3\right) - \left(2 x - 3\right)$

By doing these steps, you now have $\left(2 x - 3\right)$ to factor out.

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

The last thing you can do is factor $\left({x}^{2} - 1\right)$.

$\left(2 x - 3\right) \left(x - 1\right) \left(x + 1\right)$

Jul 4, 2017

$\left(x - 1\right) \left(2 x - 3\right) \left(x + 1\right)$

#### Explanation:

$\text{note that the coefficients sum to zero}$

$2 - 3 - 2 + 3 = 0$

$\Rightarrow \left(x - 1\right) \text{ is a factor}$

$\Rightarrow \textcolor{red}{2 {x}^{2}} \left(x - 1\right) \textcolor{m a \ge n t a}{+ 2 {x}^{2}} - 3 {x}^{2} - 2 x + 3$

$= \textcolor{red}{2 {x}^{2}} \left(x - 1\right) \textcolor{red}{- x} \left(x - 1\right) \textcolor{m a \ge n t a}{- x} - 2 x + 3$

$= \textcolor{red}{2 {x}^{2}} \left(x - 1\right) \textcolor{red}{- x} \left(x - 1\right) \textcolor{red}{- 3} \left(x - 1\right) \textcolor{m a \ge n t a}{- 3} + 3$

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

$\Rightarrow 2 {x}^{3} - 3 {x}^{2} - 2 x + 3$

$= \left(x - 1\right) \left(\textcolor{red}{2 {x}^{2} - x - 3}\right)$

$= \left(x - 1\right) \left(2 x - 3\right) \left(x + 1\right)$