SOLUTION: Use synthetic division to find the zeroes of the function f(x)=x^3+x^2+4x+4. Show all work. Thank you!

Question 1059751: Use synthetic division to find the zeroes of the function f(x)=x^3+x^2+4x+4. Show all work.
Thank you!
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Rational Roots Theorem tells you that your possible roots to check are 1, 2, 4. May the negatives of those as well. When you find your first root result, you can use either simple factoring or general solution of quadratic formula to find the next two roots.

     1    |    1   1   4   4
          |
          |        1   2   6
          ____________________________
              1    2   6   10

    2     |     1    1    4    4
          |
          |          2    6    20
          |----------------------------
               1     3    10   24

   -1    |     1    1    4    4
         |
         |         -1     0   -4
         |--------------------------
              1    0     4    0
    A root found:
x=-1 and factors are  (x+1)(x^2+4)

The synthetic divisions which gave nonzero remainder represent numbers which are NOT roots. The remainders of 0 are found when the tested value IS a root or zero.

To finish, look for the solutions for .
No need to use synthetic division for this part.

Complete Solution for the zeros of f,
.
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