Question

How do you factor `f(x)=x^3-4x^2-25x+100`?

Answer 1

`x^3 - 4x^2 - 25x+100 = (x+5)(x-5)(x-4)`

Explanation:

Start by factoring by grouping:
`x^3 - 4x^2 - 25x+100 = (x^3-4x^2)+(-25x+100)`

`= x^2(x-4)-25(x-4)`

`= (x^2-25)(x-4)`

Now we see that `x^2-25` is a difference of squares, so we can factor it too.

`= (x+5)(x-5)(x-4)`