Factor the expression. x2 + 17x + 72

Question

please help

Answer 1

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