Value of $X^4 + 9x^3+35X^2-X+4$ for $X=-5+2\sqrt{-4}$ 
Find the value of $X^4 + 9x^3+35X^2-X+4$ for $X=-5+2\sqrt{-4}$ 

Now the trivial method is to put $X=5+2\sqrt{-4}$  in the polynomial  and calculate but this is for $2$ marks only and that takes a hell lot of time for $2$! So I was thinking may be there is some trick or other technique   to get the result quicker . Can anybody help please $?$ 
Thank you .

You could consider carrying out polynomial long division, dividing the given polynomial by the minimal polynomial of $-5+4i$, which is $x^2+10x+41$. Viz:
$x^4+9x^3+35x^2-x+4=(x^2-x-4)(x^2+10x+41)+160$
We know that if $x=-5+4i$, then $x^2+10x+41$ vanishes, so the given polynomial evaluates to $160$ there.
