f(x)=2x3−5x2−4x+12f(x) = 2x^3 - 5x^2 - 4x + 12f(x)=2x3−5x2−4x+12
Use the factor theorem to show that (x−2)(x - 2)(x−2) 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:
2x3−5x2−4x+10=0 2x^3 - 5x^2 - 4x + 10 = 0 2x3−5x2−4x+10=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
Practise Edexcel AS Level Maths Algebraic Methods with exam-style questions for AS Level Maths. 35 questions covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof, matched to the Edexcel AS Level Maths (8MA0) specification and written in Paper 1 and Paper 2 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.