Question 8 - A-Level Maths

Exam Board	OCR
Module	H240/02 (Pure Mathematics and Statistics)
Year	2021
Session	November
Topic	Factor & Remainder Theorem
Type	Polynomial identity or expansion

8 The number \(K\) is defined by \(K = n ^ { 3 } + 1\), where \(n\) is an integer greater than 2 .

Given that \(n ^ { 3 } + 1 \equiv ( n + 1 ) \left( n ^ { 2 } + b n + c \right)\), find the constants \(b\) and \(c\).
Prove that \(K\) has at least two distinct factors other than 1 and \(K\).