Algebra Problem The expression $x^2-4x+5$ is a factor of $ax^3+bx^2+25$. Express the sum a+b as an integer. 
Please give an explanation of how the answer 

$ax^3+bx^2+25=(x^2-4x+5)(ax+k)$ , $k$ = constant 
$ax(x^2-4x+5) + k(x^2-4x+5) =0$ 
$ax^3 + x^2(k-4a)+x(5a-4k)+5k=0$ 
compare to original then $5k=25 \implies k=5$ 
and $(5a-4k)=0$ so $a =4$ 
and $b= k-4a = 5 -16 =-11$
