Question

How do you factor the trinomial `3r^2+2r-21`?

Answer 1

`(3r -7)(x + 3)`

Explanation:

If a trinomial can be factored, the factors of `(ax + b)(cx + d)` will give `acx^2 + (ad +bc)x + bd`. We therefore need factors of `3` and `-21` that will combine to give `2`.
The only possible factors of `3` are `3` and `1`. The appropriate factors of `-21` are `-7` and `3`
`3r^2 +2r - 21 = (3r -7)(x + 3)`