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1.3 Functions

1.3 Functions

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Question 84

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

1.3 Functions Questions

  1. A Level
  2. /Maths
  3. /1.3 Functions

181 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.

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