Question

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

Answer 1

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

Explanation:

Let `f(p) = 3p^2-2p-5`.

Notice that `f(-1) = 3+2-5 = 0`.

So `(p+1)` is a factor of `f(p)`

In order to get the `3p^2` and the `-5` terms, the other factor must be `(3p-5)` so

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