SOLUTION: Please help me to use the grouping method to completely factorize {{{ x^3 - 1

SOLUTION: Please help me to use the grouping method to completely factorize {{{ x^3 - 1 - x^2 + x }}}

Question 205846: Please help me to use the grouping method to completely factorize
Answer by dyakobovitch(40) (Show Source): You can put this solution on YOUR website!
Sure thing. To group, we need to find common factors and split the polynomial into two smaller segments. Our polynomial is: x^3 - 1 - x^2 + x. Let's rearrange it to look like x^3 - x^2 + x - 1. Now, taking our first two terms and factoring out an x^2, we have ... x^2(x-1) + 1(x-1). Notice how we have a common term (x-1), that we can factor out.

Factoring out (x-1), we have our factorized equation... x^3 - 1 - x^2 + x = (x^2+1)(x-1)
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