Question

How do you factor `x^2-12x-45`?

Answer 1

`(x-15)(x+3)`

Explanation:

Look at the colour coding to see what each part of the trinomial tells us.

`x^2 color(blue)(-) color(orange)(12)xcolor(purple)(-)color(red)(45)`

Find the factors of `color(red)(45)` which `color(purple)("subtract")` to give `color(orange)(12)`.
The signs will be `color(purple)("different")`, there must be more `color(blue)("negatives.")`
The factors of 45 which we need are 15 and 3.

`15 xx3 = 45 and15-3 = 12`

`(x-15)(x+3)`