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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 240

Given that

P(x)=64x3+96x2+44x+6 P(x) = 64x^3 + 96x^2 + 44x + 6 P(x)=64x3+96x2+44x+6
a.

Use the factor theorem to prove that (4x+1)(4x + 1)(4x+1) is a factor of P(x)P(x)P(x).

[2]
b.

Factorise P(x)P(x)P(x) completely.

[3]
c.

Hence, prove that 128n3+192n2+88n+12128n^3 + 192n^2 + 88n + 12128n3+192n2+88n+12 is a multiple of 12 when nnn is a positive whole number.

[4]
Markscheme

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

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.

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