Let L(x)=2x3−3x2−8x+12L(x) = 2x^3 - 3x^2 - 8x + 12L(x)=2x3−3x2−8x+12.
Prove that (2x−3)(2x - 3)(2x−3) is a factor of L(x)L(x)L(x).
Factorise L(x)L(x)L(x) completely.
Prove that there are no real solutions to the equation
2sin2ϕ+12cscϕ4=34sinϕ+2 \frac{2 \sin^2 \phi + 12 \csc \phi}{4} = \frac{3}{4} \sin \phi + 2 42sin2ϕ+12cscϕ=43sinϕ+2181 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.