Write x2−2x+2x^2-2x+2x2−2x+2 in the form (x−a)2+b(x-a)^2+b(x−a)2+b, where a a\,a and b b\,b are integers.
Hence prove that x2−2x+2x^2-2x+2x2−2x+2 is positive for all values of xxx
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.