Question 9 - A-Level Maths

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2024
Session	November
Topic	Polynomial Division & Manipulation

Find the quotient and remainder when \(x ^ { 4 } + 16\) is divided by \(x ^ { 2 } + 4\).
Hence show that \(\int _ { 2 } ^ { 2 \sqrt { 3 } } \frac { x ^ { 4 } + 16 } { x ^ { 2 } + 4 } \mathrm {~d} x = \frac { 4 } { 3 } ( \pi + 4 )\).