# How do you factor 2x^2 + 3x -12?

Jun 29, 2016

2(x - x1)(x - x2)

#### Explanation:

y = 2x^2 + 3x - 12
Factored form of y:
y = a(x - x1)(x - x2)
Find x1 and x2, the 2 real roots of y. Use the improved quadratic formula.
$D = {d}^{2} = {b}^{2} - 4 a c = 9 + 96 = 105$ --> $d = \pm \sqrt{105}$
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = - \frac{3}{4} \pm \frac{\sqrt{105}}{4}$
Therefor,
$y = 2 \left(x + \frac{3}{4} + \frac{\sqrt{105}}{4}\right) \left(x + \frac{3}{4} - \frac{\sqrt{105}}{4}\right)$