Question

How do you factor `x^2+17x+72`?

Answer 1

`(x+8)(x+9)`
When you factor a quadratic expression where the number in front of the square term is `1`, you are looking for two numbers whose product equals the last term and whose sum equals the middle term.

Take the equation: `x^2 + 17x + 72`

We are looking for two numbers with a product of `72` and with a sum of `17`. Which two numbers are those?

If you thought `8` and `9` you would be correct.
`x^2 + 17x + 72 = (x+8)(x+9)`

Let's redistribute it to check:
`(x+8)(x+9)`
`(x^2+9x+8x+72)`
`(x^2+17x+72)`

It works, and I hope that was helpful.