How do you factor x^6-26x^3-27?

1 Answer
Feb 5, 2015

First let's notice that x^6=(x^3)^2

Let r=x^3

Using substitution we have

r^2-26r-27

We now look for the factors of -27 that will combine (add) to make -26

We find that -27 and 1 multiply to be -27 and add to be -26. This gives us

(r-27)(r+1)

Now substitute x^3 back in for r

(x^3-27)(x^3+1)

We should recognize this as a difference of cubes and a sum of cubes.

(x-3)(x^2+3x+9)(x+1)(x^2-x+1)