How do you factor x^5-5x^3-36x completely?

1 Answer
Feb 5, 2015

We need to start out by factoring out any common factors. We notice that we can factor out x.

x(x^4-5x^2-36)

Note that x^4=(x^2)^2

x((x^2)^2-5x^2-36)

Let r=x^2

x(r^2-5r-36)

Now factor (r^2-5r-36)

x(r-9)(r+4)

Replace r with x^2

x(x^2-9)(x^2+4)

We should recognize (x^2-9) as a difference of squares.

Leaving me with

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