Let f(x)=6x3+13x2−4x−15f(x) = 6x^3 + 13x^2 - 4x - 15f(x)=6x3+13x2−4x−15.
Use the factor theorem to show that (2x+3)(2x + 3)(2x+3) is a factor of f(x)f(x)f(x).
Hence, using algebra, write f(x)f(x)f(x) as a product of three linear factors.
Solve, for π2<θ<π\frac{\pi}{2} < \theta < \pi2π<θ<π, the equation 6tan3θ+13tan2θ−4tanθ−15=06\tan^3 \theta + 13\tan^2 \theta - 4\tan \theta - 15 = 06tan3θ+13tan2θ−4tanθ−15=0 giving your answers to 3 significant figures.
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.