Question 1204777
This is a very routine exercise.  Almost to fitting a formula!


{{{(x-(5+2i))(x-(5-2i))(x+1)^2}}}
Carry through all the multiplication and simplifications....



{{{(x-5-2i)(x-5+2i)(x+1)^2}}}

{{{((x-5)-2i)((x-5)+2i)(x^2+2x+1)}}}

{{{((x-5)^2-(2i)^2)(x^2+2x+1)}}}, recognize what makes Difference Of Two Squares

{{{(x^2-10x+25-4i^2)(x^2+2x+1)}}}

{{{(x^2-10x+25-4(-1))(x^2+2x+1)}}}, understand meaning of i^2

{{{(x^2-10x+29)(x^2+2x+1)}}}


Choosing lattice form for the polynomial multiplication
<pre>
            x^2        2x        1
--------------------------------------------
x^2    |    x^4         2x^3      x^2
       |
-10x   |   -10x^3      -20x^2     -10x
       |
29     |  29x^2         58x       29
</pre>
Resulting in  {{{highlight(x^4-8x^3+10x^2+48x+29)}}}