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

May 22, 2015

You can find its roots and then turn them into factors. I"ll use Bhaskara to find the roots.

$\frac{- 3 \pm \sqrt{9 - 4 \left(2\right) \left(- 2\right)}}{4}$
$\frac{- 3 \pm 5}{4}$
${x}_{1} = - 2$, which is the same as the factor $x + 2 = 0$
${x}_{2} = \frac{1}{2}$, which is the same as the factor $2 x - 1 = 0$

Thus,

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

May 29, 2015

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

Product = - 4
Sum = +3
Factors = 4, - 1
=

So spiting it up

$2 {x}^{2} - x + 4 x - 2$

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

Hence factored