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Algebraic Methods

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Question 216

A discrete model for the total number of stable configurations, N(k)N(k)N(k), of a crystal lattice with k k\,k layers is given by

N(k)=10k3+11k2+7k+2 N(k) = 10k^3 + 11k^2 + 7k + 2 N(k)=10k3+11k2+7k+2
a.

Use the factor theorem to show that (2k+1)(2k + 1)(2k+1) is a factor of N(k)N(k)N(k).

[2]
b.

Express N(k)N(k)N(k) in the form

N(k)=(2k+1)(ak2+bk+c) N(k) = (2k + 1)(ak^2 + bk + c) N(k)=(2k+1)(ak2+bk+c)

where aaa, b b\,b and c c\,c are constants to be found.

[3]
c.

Given that n n\,n is a positive integer, use your answer to part (b) to explain why 10n3+11n2+7n+210n^3 + 11n^2 + 7n + 210n3+11n2+7n+2 is never prime.

[2]
Markscheme

Algebraic Methods Questions

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

368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.

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