The pressure P P\,P in a specialized hydraulic chamber is modeled by the cubic function
P(x)=kx3−11x2−26x+24 P(x) = kx^3 - 11x^2 - 26x + 24 P(x)=kx3−11x2−26x+24where x x\,x represents the displacement of a control valve in millimetres and k k\,k is a design constant.
Given that (x+2)(x + 2)(x+2) is a factor of P(x)P(x)P(x), show that k=4k = 4k=4.
Using algebra and showing each step of your working, fully factorise P(x)P(x)P(x).
Solve, for 0∘≤θ<360∘0^\circ \le \theta < 360^\circ0∘≤θ<360∘, the equation
4cos3θ−11cos2θ−26cosθ+24=0 4\cos^3 \theta - 11\cos^2 \theta - 26\cos \theta + 24 = 0 4cos3θ−11cos2θ−26cosθ+24=0giving your answers to one decimal place.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.