Question 1039732
Use synthetic division to check on possible roots,  -1, -2, -4.  Expect one of them to be repeated.


<pre>
-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
</pre>


Quadratic Factor {{{x^2+1}}}, and linear binomial factors  {{{(x+2)}}} with multiplicity two.  The quadratic may be stated  {{{(x+i)(x-i)}}}.
Your h(x) is  {{{highlight((x+2)^2(x+i)(x-i))}}}.