Question

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

Answer 1

`(2x-3)(x+1)`

Explanation:

Combine the factors of 2 and 3 so by subtracting you get 1.
The middle term is `color(red)(1)x`

Write the factors and find the cross-products:
`color(white)(x.xx)(2)" "(3)`
`color(white)(xxxx)2" "3 rArr 1xx3 = 3`
`color(white)(xxxx)1" "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)

`color(white)(xxxx)2" "-3 rArr 1xx-3 = -3`
`color(white)(xxxx)1" "+1 rArr 2xx+1 = +2" "-3+2=-1`

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

`(2x-3)(x+1)`