# Question 13

\begin{align} & \text{The remainder when }6{{p}^{3}}-{{p}^{2}}-47p+30\text{ is divided by }p-3\text{ is } \\ & \text{(A) }21\text{ (B) 42 (C) 63 (D) 18} \\\end{align}
\begin{align} & \text{Let }f(p)=6{{p}^{3}}-{{p}^{2}}-47p+30 \\ & \text{The remainder when }f(p)\text{ is divided by }p-3\text{ is }f(3) \\ & f(3)=6{{(3)}^{3}}-{{3}^{2}}-47(3)+30 \\ & f(3)=162-9-141+30=42 \\ & \text{The remainder is 3} \\\end{align}