<s>[INST] Polynomial division with remainder 
If the polynomial
  $$x^4-x^3+ax^2+bx+c$$
  divided by the polynomial
  $$x^3+2x^2-3x+1$$
  gives the remainder $$3x^2-2x+1$$
  then how much is (a+b)c?

So what I know, and how I solved these problems before, I can write this down like this:
$x^4-x^3+ax^2+bx+c=Q(x)(x^3+2x^2-3x+1)+3x^2-2x+1$
And from here I should get the roots of $x^3+2x^2-3x+1$ so I could use the remainder only since I don't know $Q(x)$
$x^3+2x^2-3x+1=0$
but I can't find the roots of this by hand, so I used WolframAlpha to get the roots, but they are not whole numbers so I couldn't write this in the form of $(x-x_1)(x-x_2)(x-x_3)$ and then just use $P(x_1)$, $P(x_2)$, $P(x_3)$ to get $a,b,$ and $c$
I tried regular dividing on these polynomials to get $Q(x)$ but I couldn't divide them because of the $a,b$ and $c$ present
 [/INST] Hint: Compute the remainder of $x^4-x^3$ when divided by $x^3+2x^2-3x+1$.
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