# Is it possible to factor y= 2x^2 + 5x - 3 ? If so, what are the factors?

May 29, 2018

$\left(x + 3\right) \left(2 x - 1\right)$

#### Explanation:

$\text{using the a-c method to factor the quadratic}$

$\text{the factors of the product } 2 \times - 3 = - 6$

$\text{which sum to + 5 are + 6 and - 1}$

$\text{split the middle term using these factors}$

$2 {x}^{2} + 6 x - x - 3 \leftarrow \textcolor{b l u e}{\text{factor by grouping}}$

$= \textcolor{red}{2 x} \left(x + 3\right) \textcolor{red}{- 1} \left(x + 3\right)$

$\text{take out the "color(blue)"common factor } \left(x + 3\right)$

$= \left(x + 3\right) \left(\textcolor{red}{2 x - 1}\right)$

$2 {x}^{2} + 5 x - 3 = \left(x + 3\right) \left(2 x - 1\right)$