Question

how do I solve 2a^2-a-21=0 by factoring?

Answer 1

You have to first observe the -21.
You have to find numbers which you can multiply together to get 21.

Those numbers are:
1 * 21
3 * 17

Now observe the the -a and the 2a^2. You know you need a factor that looks like
(2a + b)(a + n)
What combination of numbers will give you a -a as your middle term?

I know you're familiar with factoring equations like

x^2 + 3x + 2 = (x+2)(x+1) = x^2 + x + 2x + 2

Same thing applies here. You just need to choose between these following options. Only one of them is right but you'll find that out by FOILing. I know the answer but you should FOIL it yourself to find the right answer. I hope that helps.

(2a^2 - 21)(a - 1)
(2a^2 - 1)(a - 21)
(2a^2 - 7)(a + 3)
(2a^2 - 3)(a + 7)

Answer 2

Thanks!

Answer 3

You're welcome!