# Is it possible to factor y=3x^2 +10x - 8 ? If so, what are the factors?

May 10, 2016

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

#### Explanation:

In order to factor this expression you need to find factors of 3 and 8 that add or subtract to give 10. Because the middle term is positive and the last term is negative the result must be arrived at by subtraction.

The factors of $3$ can only be $3$ and $1$. The factors of $8$ can be $8$ and $1$ or $4$ and $2$.
By trial and error you can get $3 \cdot 4 = 12$ and $1 \cdot 2 = 2$. $12 - 2 = 10$

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