A1. Which polynomial must you divide by the polynomial $q(x)=3 x-5$ to get the quotient $k(x)=x^{2}-2 x+7$ and the remainder $r(x)=2$?
(A) $p(x)=3 x^{3}-2 x+7$
(B) $p(x)=3 x^{3}-11 x-33$
(C) $p(x)=3 x^{3}-11 x^{2}+31 x-33$
(D) $p(x)=3 x^{3}+11 x^{2}+31 x-33$

(E) None of the above answers is correct.
A1. We consider the fundamental theorem of polynomial division: $p(x)=k(x) \cdot q(x)+r(x)$. We substitute $k(x)$, $q(x)$, and $r(x)$, multiply and add, and obtain $p(x)=3 x^{3}-11 x^{2}+31 x-33$.