# How do you factor 2x^2 - 5x - 3?

May 7, 2018

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

#### Explanation:

$2$ only factors one way, $2 = 2 \times 1$. So if there is a possible factorization, it looks like

$\left(2 x + \textrm{c o n s \tan t}\right) \left(x + \textrm{c o n s \tan t}\right)$

The two constants multiply to $- 3$ and similarly, $- 3 = 3 \times - 1 = - 3 \times 1$ are the only possibilities for that. So we get four possibilities for a factorization (the first constant can be $- 3 , - 1 , \quad 1 , \mathmr{and} 3$) and we quickly find

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