Express n3−k2nn^3 - k^2nn3−k2n as a product of three factors, in terms of kkk.
Given that n n\,n and k k\,k are positive integers, where k k\,k is coprime to 6, prove that n3−k2nn^3 - k^2nn3−k2n is a multiple of 6
257 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof. Each one has a worked solution and a mark scheme showing where the marks go.