Find the remainder when $f(x) = x^{2016}+2x^{2015}-3x+4$ is divided by $g(x)=x^2+3x+2$ Find the remainder when $f(x) = x^{2016}+2x^{2015}-3x+4$ is divided by $g(x)=x^2+3x+2$ 
I try to factor them, but I failed. I know that it's impossible to divide it

Notice: $x^2+3x+2=(x+1)(x+2)$ and let the remainder be $ax+b$ (must be at most linear since we divide by quadratic polynomial).
Write $$x^{2016}+2x^{2015}-3x+4=k(x)(x+2)(x+1)+ax+b$$
Put $x=-1$ we get $$6=-a+b$$ and put $x=-2 $ we get $$10 = -2a+b$$ Now solve this system and you get an answer.
