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

Aug 18, 2016

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

Explanation:

Combine the factors of 2 and 3 so by subtracting you get 1.
The middle term is $\textcolor{red}{1} x$

Write the factors and find the cross-products:
$\textcolor{w h i t e}{x . \times} \left(2\right) \text{ } \left(3\right)$
$\textcolor{w h i t e}{\times \times} 2 \text{ } 3 \Rightarrow 1 \times 3 = 3$
$\textcolor{w h i t e}{\times \times} 1 \text{ "1 rArr 2xx1 = 2" } 3 - 2 = 1$

We have the correct factors, now sort out the signs:
We need to end up with -1. (more negatives)

$\textcolor{w h i t e}{\times \times} 2 \text{ } - 3 \Rightarrow 1 \times - 3 = - 3$
$\textcolor{w h i t e}{\times \times} 1 \text{ "+1 rArr 2xx+1 = +2" } - 3 + 2 = - 1$

The top row is the first bracket and the bottom row is the second bracket.

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