f(x)=x^3-4x^2-x+4

Question

How do I find the x-intercept for this?

This is from my book:
step 1: 0=x^3-4x^2-x+4
step 2: 0=x^2(x-4)+(-1)(x-4)
step 3: 0=(x^2-1)(x-4)

I know how to solve once I get to step 3, but in step 2, I don't know what they've done or why. Where does that (-1) come from? Why is it (x-4)?

Please help explain this to me. I'd be really thankful.

Answer 1

step 1: 0=x^3-4x^2-x+4

we would like to factor that.
rewrite as
x^3-4x^2 - (x-4)
now you can see that I can factor an (x-4) out of the first two terms
x^2 (x-4) - (x-4)
which is
x^2 (x-4) -1 (x-4)

step 2: 0=x^2(x-4)+(-1)(x-4)
step 3: 0=(x^2-1)(x-4)