# How do you factor 6x^2-10x+24?

May 16, 2016

$2 \left(3 {x}^{2} - 5 x + 12\right)$

#### Explanation:

$f \left(x\right) = 2 y = 2 \left(3 {x}^{2} - 5 x + 12\right)$
Factor y, the trinomial in parentheses, by the new AC Method (Socratic Search)
$y = 3 {x}^{2} - 5 x + 12$
$D = {b}^{2} - 4 a c = 25 - 144 = - 119.$
Since D < 0, this trinomial y can't be factored.
$f \left(x\right) = 2 y = 2 \left(3 {x}^{2} - 5 x + 12\right)$