Question

How do you factor the trinomial `5x^2 − 2x − 7`?

Answer 1

`5x^2-2x-7` factors to `(5x + 1)(x-7)`

Explanation:

Since both 5 and 7 are prime,
the only options for
`5x^2` are `1x` and `5x`,

and the only options for
`-7` are `-1` and `7` or `1` and `-7`

Notice that the middle term is `-2x` and to get that we would need to have had `5x-7x`, before simplifying the middle term.

So to get this is a factored form it would be
`(5x - 1)(x+7)`