Question

How do you factor `x^3 +5x^2-9x-45`?

Answer 1

`(x+3)(x-3)(x+5)`

Explanation:

Note that `(-9x-45)= (-9)color(blue)((x+5))`
and that `(x^3+5x^2) = (x^2)color(blue)((x+5))`

We can write
`x^3+5x^2-9x-45`
`color(white)("XXX")=(x^2-9)color(blue)((x+5))`

If we further note that `(x^2-9)` is the difference of squares `color(green)((x+3))color(brown)((x-3))`
we can expand this to
`x^3+5x-9x-45`
`color(white)("XXX")=color(green)((x+3))color(brown)((x-3))color(blue)((x+5))`