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:
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 $Q(x)$
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