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

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Answer 1 · 2015-02-05T04:18:42

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)#