Let p(x)=12x3−8x2−3x+2p(x) = 12x^3 - 8x^2 - 3x + 2p(x)=12x3−8x2−3x+2.
Prove that (2x−1)(2x - 1)(2x−1) is a factor of p(x)p(x)p(x).
Factorise p(x)p(x)p(x) completely.
Prove that there are no real solutions to the equation
12sec2θ+2cosθ3=83secθ+1 \frac{12 \sec^2 \theta + 2 \cos \theta}{3} = \frac{8}{3} \sec \theta + 1 312sec2θ+2cosθ=38secθ+1181 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.