# How do you factor 5x^2-11x+2?

Aug 10, 2015

Factor y = 5x^2 - 11x + 2.

Ans: (5x - 1)(x - 2).

#### Explanation:

I use the new AC Method to factor trinomials (Socratic Search).
$y = 5 {x}^{2} - 11 x + 2 =$ 5(x + p)(x + q)
Converted trinomial:
$y ' = {x}^{2} - 11 x + 10 =$ (x + p')( x = q').
Find p' and q' knowing sum (b = - 11) and product (ac = 10).
They are: p' = -1, and q' = -10
Therefor: $p = \frac{p '}{a} = - \frac{1}{5}$, and q = (q')/a = -10/5 = -2
Factored form of y:
$y = 5 \left(x - \frac{1}{5}\right) \left(x - 2\right) = \left(5 x - 1\right) \left(x - 2\right)$