Question

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

Answer 1

`2x^2 - 5x - 3 = (2x + 1)(x - 3)`

Explanation:

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

`(2x + text{constant})(x + text{constant})`

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, or 3`) and we quickly find

`2x^2 - 5x - 3 = (2x + 1)(x - 3)`