f(x)=2x3−x2−4x+3f(x) = 2x^3 - x^2 - 4x + 3f(x)=2x3−x2−4x+3
Use the factor theorem to show that (x−1)(x - 1)(x−1) is a factor of f(x)f(x)f(x).
Hence, show that f(x)=0f(x) = 0f(x)=0 only has two distinct real roots
Sketch the graph of y=f(x)y = f(x)y=f(x)
Deduce, giving a reason for your answer, the number of real roots of the equation:
2x3−x2−4x+1=0 2x^3 - x^2 - 4x + 1 = 0 2x3−x2−4x+1=0Given that k k\,k is a constant and the curve with equation y=f(x+k)y = f(x + k)y=f(x+k) passes through the origin, find the two possible values of kkk
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.