# How do you factor completely 3x^2-x-10 ?

Apr 29, 2016

(3x + 5)(x - 2)

#### Explanation:

Use the systematic new AC method (Socratic Search)
$y = 3 {x}^{2} - x - 10 = 3 \left(x + p\right) \left(x + q\right)$
Converted trinomial $y ' = {x}^{2} - x - 30 =$ (x + p')(x + q')
p' and q' have opposite signs, because ac < 0.
Factor pairs of (ac = -30) --> (-5, 6)(5, -6). This sum is -1 = b. Therefor, p' = 5 and q' = -6.
Back to original y, $p = p \frac{'}{a} = \frac{5}{3}$ and $q = \frac{q '}{a} = - \frac{6}{3} = - 2$
Factored form:
$y = 3 \left(x + \frac{5}{3}\right) \left(x - 2\right) = \left(3 x + 5\right) \left(x - 2\right)$