f(x)=x3−x2+x−1f(x) = x^3 - x^2 + x - 1f(x)=x3−x2+x−1
Use the factor theorem to show that (x−1)(x - 1)(x−1) is a factor of f(x)f(x)f(x).
Show that f(x)=0f(x) = 0f(x)=0 only has one real root.
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.