SOLUTION: How do I fully factor this? {{{x^5 -x^3 + 27x^2 -27}}} My attempt: I took x^3 and 27 to put them in one place. They factor into {{{(x + 3) (x^2 - 3x + 9) }}} However, t

Algebra ->  Expressions-with-variables -> SOLUTION: How do I fully factor this? {{{x^5 -x^3 + 27x^2 -27}}} My attempt: I took x^3 and 27 to put them in one place. They factor into {{{(x + 3) (x^2 - 3x + 9) }}} However, t      Log On


   



Question 903819: How do I fully factor this?
x%5E5+-x%5E3+%2B+27x%5E2+-27
My attempt:
I took x^3 and 27 to put them in one place. They factor into
%28x+%2B+3%29+%28x%5E2+-+3x+%2B+9%29+
However, the full answer is
%28x%2B3%29+%28x%5E2+-+3x+%2B+9%29+%28x-1%29%28x%2B1%29
What are the steps on fully factoring this?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E5+-x%5E3+%2B+27x%5E2+-27

%28x%5E5+-x%5E3%29+%2B+%2827x%5E2+-27%29 Group

x%5E3%28x%5E2+-1%29+%2B+27%28x%5E2+-1%29 Factor each group

%28x%5E3%2B27%29%28x%5E2+-1%29 Factor out x%5E2-1

%28x%2B3%29%28x%5E2-3x%2B9%29%28x%5E2+-1%29 Factor x%5E3%2B27 (use sum of cubes rule)

%28x%2B3%29%28x%5E2-3x%2B9%29%28x-1%29%28x%2B1%29 Factor x%5E2-1 (use difference of squares rule)