Question

What is the complete factorization of the polynomial below? X3-4x^2+x-4

Answer 1

Answer:  (x - 4)(x - (i))(x + (i))

Step-by-step explanation:

This factoring job lends itself well to synthetic division.  Looking at the constant term, -4, I came up with several possible roots based upon -4:  {±1, ±2, ±4}.  I chose +4 as my first trial root.  Sure enough, there was a zero remainder, which indicated that 4 is a root of this polynomial and (x - 4) is a factor.  The coefficients of the trinomial quotients are 1   0   1, which indicates a quotient of x^2 + 1, which has the following roots:  x = +(i) and x = -(i)

So the complete factorization of the polynomial is (x - 4)(x - (i))(x + (i)).

4   )   1    -4    1    -4

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Answer:

      1