SOLUTION: .1 h(x) = x^4 + 4x^3 + 5x^2 + 4x + 4. Write the polynomial as the product of linear factors? List all the zeros of the function. (Enter your answers as a comma-separated list.)

Algebra ->  Equations -> SOLUTION: .1 h(x) = x^4 + 4x^3 + 5x^2 + 4x + 4. Write the polynomial as the product of linear factors? List all the zeros of the function. (Enter your answers as a comma-separated list.)      Log On


   

Question 1039732: .1 h(x) = x^4 + 4x^3 + 5x^2 + 4x + 4.
Write the polynomial as the product of linear factors?
List all the zeros of the function. (Enter your answers as a comma-separated list.)?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Use synthetic division to check on possible roots, -1, -2, -4. Expect one of them to be repeated. 

-4   |   1   4   5   4   4
     |
     |      -4   0  -20  64
     |____________________________
        1    0   5  -16   68



-2   |   1    4    5    4    4
     |
     |       -2    -4   -2   -4
     |_______________________________
        1     2    1    2    0


Now possible roots to test are only  -1 and -2.


-2   |    1    2    1    2
     |
     |        -2    0    -2
     |____________________________
         1     0    1     0


Quadratic Factor x%5E2%2B1, and linear binomial factors %28x%2B2%29 with multiplicity two. The quadratic may be stated %28x%2Bi%29%28x-i%29.
Your h(x) is highlight%28%28x%2B2%29%5E2%28x%2Bi%29%28x-i%29%29.