How do you solve 2x^2-5x-3 by factoring?

Apr 3, 2018

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

Explanation:

$2 x 3 = 6$ so then you must find two numbers (a negative and a positive since there are two negatives in the original problem) that will add up to $5$ and multiply to $6$.

The numbers are then $- 6$ and $+ 1$ which gives you:

$2 {x}^{2} + 1 x - 6 x - 3$

Split down the middle and factor out an $x$ and a $- 3$

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

Take the leading coefficients and you'll finish with

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

Hope this helps!