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 A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 261 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 A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 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.
