Hi Arlene.

You need to factor the quadratic expression x² + 2x - 24 to solve this question. Then you will have two factors that, when multiplied together, give zero. When you multiply two quantities and get zero, you know that one or the other (or both) have to be zero, so you can then split them up. I'll show you what I mean with a similar problem.

Solve: x² - 9x - 36 = 0.

First I try to find two numbers that I can multiply together to get 36:
1, 36
2, 18
3, 12
4, 9
6, 6

Now I look at this list and see if there is a difference of 9 in any pair, or if the pair might add up to 9.

I can see that 3 and 12 are different by 9. So I will try to set up the signs (plus and minus) so that when I multiply, I get -36 and when I add them, I get -9.

It works for -12 and +3. So I can now write the factors:

(x - 12) (x + 3)

I can use FOIL to check that this is really the same as the original expression:

(x - 12) (x + 3) = (x)(x) - 12(x) + 3(x) - 12(3) = x² - 9x - 36. Good.

So (x - 12) (x + 3) = 0, therefore one of the factors must equal zero.

Either x - 12 = 0 or x + 3 = 0.

If x - 12 = 0, then x = 12. If x + 3 = 0, then x = -3.

So if x = 12 or -3, then x² - 9x - 36 = 0. That's the answer.

Try the same idea for your question, Arlene.

Cheers,
Stephen La Rocque.