Binomial factors?

Question

Find the binomial factors for each trinomial

24a^2 + 5a -1

the answer sheet looks like this:


(24a ) (a )

Answer 1

You need factors of -24 (the product of the outside and inside) that add to 5. That would be 8 and -3. If you rewrite the trinomial 24a^2 +8a-3a-1 you can factor by grouping:
8a(3a+1)-1(3a+1) = (3a+1)(8a-1).

Answer 2

Good for the answer sheet. The trinomial factors
(8a-1)(3a+1)

Answer 3

(8a -1)(3a +1)