# Is it possible to factor y=3x^2+2x-8 ? If so, what are the factors?

Apr 19, 2018

$y = \left(x + 2\right) \left(3 x - 4\right)$

#### Explanation:

$y = 3 {x}^{2} + 2 x - 8$

to begin the factorising process

we look for factors of $3 \times - 8 = - 24$

that sum to the middle term $2$

by inspection we will have $+ 6 , - 4$

#we now split teh middle term with these factors and factorise by grouping

$y = 3 {x}^{2} + 6 x - 4 x - 8$

$y = \left(3 {x}^{2} + 6 x\right) - \left(4 x + 8\right)$

$y = 3 x \left(x + 2\right) - 4. \left(x + 2\right)$

$y = \left(x + 2\right) \left(3 x - 4\right)$