Factored form of 2a^2-21a-65

Question

I don't understand, how do you find the factored form when there's a  2x^2

Answer 1

2a^2 - 21a - 65

We should end up with something like (?a + ?)(?a + ?)

The only way to make 2 (out of whole numbers) is 2 * 1, so we should have (2a + ?)(a + ?)

We can make 65 with 1 * 65 and 5 * 13.  Let's try 5 * 13.  Notice that 5*1 - 13*2 = -21, which we want for the a.

(2a + ?)(a + ?)

(2a + 5)(a - 13)

Check it with FOIL:

2a^2 + 2a(-13) + 5(a) + 5(-13)

2a^2 - 26a + 5a - 65

2a^2 - 21a - 65

It matches the original problem, so it works.

Answer:  (2a+5)(a-13)