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Algebraic Methods

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Question 111

Let L(x)=2x3−3x2−8x+12L(x) = 2x^3 - 3x^2 - 8x + 12L(x)=2x3−3x2−8x+12.

a.

Prove that (2x−3)(2x - 3)(2x−3) is a factor of L(x)L(x)L(x).

[2]
b.

Factorise L(x)L(x)L(x) completely.

[3]
c.

Prove that there are no real solutions to the equation

2sin⁡2ϕ+12csc⁡ϕ4=34sin⁡ϕ+2 \frac{2 \sin^2 \phi + 12 \csc \phi}{4} = \frac{3}{4} \sin \phi + 2 42sin2ϕ+12cscϕ​=43​sinϕ+2
[4]

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