SOLUTION: Factor the polynomial function over the complex numbers. {{{ f(x) = x^4 - x^3 - 2x

SOLUTION: Factor the polynomial function over the complex numbers. {{{ f(x) = x^4 - x^3 - 2x - 4 }}} f(x) =

Question 1127861: Factor the polynomial function over the complex numbers.

f(x) =
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Remember that "complex numbers" includes real numbers. So look for rational roots first.

Substitution show f(-1)=0, so -1 is a root. Extract that root using synthetic division.


   -1 |  1 -1  0 -2 -4
      |    -1  2 -2  4
      ----------------
        1  -2  2 -4  0

The remaining polynomial is . A second real root can be found using factoring by grouping.

The remaining quadratic factor can be factored over the complex numbers as

So the complete factorization over the complex numbers is

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