x^2 + 17x + 72
(x )(x )
What times what makes 72?
1 * 72
2 * 36
and so on.
But what do they add up to?
1 * 72 = 72, 1+72 = 73
2 * 36 = 72, 2 + 36 = 38
3 * 24 = 72, 3 + 24 = 27
4 * 18 = 72, 4 + 18 = 22
6 * 12 = 72, 6 + 12 = 18
8 * 9 = 72, 8 + 9 = 17
Ah. . .17 is our middle term in x^2 + 17x + 72, so we can do this:
(x+8)(x+9) = x^2 + 17x + 72