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 

If $x^2-4x+5$ is a factor of $ax^3+bx^2+25$, then $ax^3+bx^2+25=(x^2-4x+5)(\text{something})$.  Since $ax^3+\cdots$ is a polynomial of degree 3 and $x^2-\cdots$ is a polynomial of degree 2, the "something" must be a polynomial of degree 1:
$$ax^3+bx^2+0x+25=(x^2-4x+5)(\underline{\;\;\;\;\;\;}x+\underline{\;\;\;\;\;\;})$$
Try to fill in the two blanks based the terms on the left side that don't have $a$ and $b$ in them (for example, how will $+25$ end up in the product?), then finish the multiplication to find the values of $a$ and $b$.
