# How do you factor 3x^2 - 10 + 3 = 0?

Mar 27, 2016

(3x - 1)(x - 3)

#### Explanation:

Use the new AC Method (Socratic).
$y = 3 {x}^{2} - 10 + 3 =$ 3(x + p)(x + q)
Converted $y ' = {x}^{2} - 10 x + 9 =$ (x + p')(x + q').
Find p' and q' knowing sum (-10) and product (9). They are: p' = -1 and q' = -9.
Back to y --> $p = \frac{p '}{a} = - \frac{1}{3}$ and $q = \frac{q '}{a} = - \frac{9}{3} = - 3.$
Factored form y = 3(x - 1/3)(x- 3) = (3x - 1)(x - 3)