When factoring a quadratic that starts with X^2, you want to find the 2 numbers that both:
1. Multiply to the number that doesn't have an x. 36 in this case.
2. Add up to the number that is in the middle. This would be 13 in this problem.
You will just have to go through the factors of the last number to see what adds up to the middle number, but you should get 4 and 9 in this problem.
Now, your teacher may teach a different way of doing this step, but it is basically the same step. I usually split the middle into the two numbers like so:
[tex] {x}^{2} + 4x + 9x + 36[/tex]
. Then I take the common factors out like this:
[tex]x(x + 4) + 9(x + 4)[/tex]
And since they share the coefficient of (x+4), you can factor it out into
[tex](x + 4)(x + 9)[/tex]
.
