Question

How do you factor `x^3+9x^2+15x-25`?

Answer 1

`x^3+9x^2+15x-25 = (x-1)(x+5)^2`

Explanation:

Given:

`x^3+9x^2+15x-25`

First notice that the sum of the coefficients is `0`. That is:

`1+9+15-25 = 0`

Hence `x=1` is a zero and `(x-1)` a factor:

`x^3+9x^2+15x-25 = (x-1)(x^2+10x+25)`

To factor the remaining quadratic note that both `x^2` and `25 = 5^2` are perfect squares, with `10x = 2(5)x`. So this quadratic is a perfect square trinomial:

`x^2+10x+25 = x^2+2(5)x+5^2 = (x+5)^2`

Putting it all together:

`x^3+9x^2+15x-25 = (x-1)(x+5)^2`