Prove that x2−2(1+2)x+7x^2 - 2(1+\sqrt{2})x + 7x2−2(1+2)x+7 is positive for all values of xxx, giving its minimum value in exact form.
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.