# How do you factor 3x^2 + 5x - 28?

Apr 21, 2016

$3 {x}^{2} + 5 x - 28 = \left(3 x - 7\right) \left(x + 4\right)$

#### Explanation:

$3 {x}^{2} + 5 x - 28 = \left(3 x - 7\right) \left(x + 4\right)$

Apr 21, 2016

(3x - 7)(x + 4)

#### Explanation:

Use the new AC method to factor trinomials (Socratic Search)
$y = 3 {x}^{2} + 5 x - 28 =$ 3(x + p)(x + q)
$C o n v e r t e d t r \in o m i a l y ' = {x}^{2} + 5 x - 84 =$ (x + p')(x + q')
p' and q' have opposite signs, because ac < 0.
Factor pairs of (ac = -84) -->...(-4, 21)(-7, 12). This sum is 5 = b. Then, p' = -7 and q' = 12.
Back to y, $p = \frac{p '}{a} = - \frac{7}{3}$ and $q = \frac{q '}{a} = \frac{12}{3} = 4.$
Factored form:
$y = 3 \left(x - \frac{7}{3}\right) \left(x + 4\right) = \left(3 x - 7\right) \left(x + 4\right)$