Question 11
(SWE 6) Let $P,Q,R$ be polynomials and let $S(x)=P(x^3)+xQ(x^3)+x^2R(x^3)$ be a polynomial of degree $n$ whose roots $x_1,\ldots,x_n$ are distinct. Construct with the aid of the polynomials $P,Q,R$ a polynomial $T$ of degree $n$ that has the roots $x_1^3,x_2^3,\ldots,x_n^3$.