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Algebraic Methods

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Question 106

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+24

where x x\,x represents the displacement of a control valve in millimetres and k k\,k is a design constant.

a.

Given that (x+2)(x + 2)(x+2) is a factor of P(x)P(x)P(x), show that k=4k = 4k=4.

[2]
b.

Using algebra and showing each step of your working, fully factorise P(x)P(x)P(x).

[3]
c.

Solve, for 0∘≤θ<360∘0^\circ \le \theta < 360^\circ0∘≤θ<360∘, the equation

4cos⁡3θ−11cos⁡2θ−26cos⁡θ+24=0 4\cos^3 \theta - 11\cos^2 \theta - 26\cos \theta + 24 = 0 4cos3θ−11cos2θ−26cosθ+24=0

giving your answers to one decimal place.

[3]

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 226 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, 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.

Question bank