Express (n−1)n(n+1)(n-1)n(n+1)(n−1)n(n+1) as a polynomial in nnn.
Given that n n\,n is a positive integer, prove that (n−1)n(n+1)(n-1)n(n+1)(n−1)n(n+1) 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.