Prove that n2+8n+19>2n+3n^2 + 8n + 19 > 2n + 3n2+8n+19>2n+3 is true for all values of nnn, and find the exact minimum value of n2+8n+19n^2 + 8n + 19n2+8n+19 and the value of n n\,n at which it occurs.
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.