Question

How do you factor `z^2+15z+36`?

Answer 1

Find two numbers that multiply to `36` and add to `15`, then expand it using the two numbers as coefficients of `z`.

Of the factors of `36`, `12` and `3` are the only two that add to `15`.

`z^2+3z+12z+36`

`(z^2+3z)+(12z+36)`

`z(z+3)+12(z+3)`

`(z+3)(z+12)`