Let f(x)=36x3−27x2−4x+3f(x) = 36x^3 - 27x^2 - 4x + 3f(x)=36x3−27x2−4x+3.
Use the factor theorem to show that (3x−1)(3x - 1)(3x−1) is a factor of f(x)f(x)f(x).
Express f(x)f(x)f(x) as a product of three linear factors.
A mechanical engineer modeling the resonance of a suspension bridge determines that the equilibrium angles θ\thetaθ are given by the equation: 12sec2θ+cosθ4=2.25secθ+13\frac{12\sec^2 \theta + \cos \theta}{4} = 2.25\sec \theta + \frac{1}{3}412sec2θ+cosθ=2.25secθ+31 Prove that there are no real values of θ\thetaθ that satisfy this stability condition.
Practise Edexcel A Level Maths 1.5 Algebraic Division with exam-style questions for A Level Maths. 65 questions, 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.