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=0 6\tan^3 \theta + 13\tan^2 \theta - 4\tan \theta - 15 = 0 6tan3θ+13tan2θ−4tanθ−15=0giving your answers to 3 significant figures.
181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.