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 .

$X+5=4i$ squaring you get $x^2+10x+41=0$ now just divide the given polynomial with this equation so solving $$\frac{x^4+9x^3+35x^2-x+4}{x^2+10x+41}$$ you get it equal to $(160)$ 
