The mechanical stress S S\,S measured in a reinforced composite beam depends on a reinforcement parameter k k\,k and is modeled by the function:
S(k)=10k3+9k2+10k+4 S(k) = 10k^3 + 9k^2 + 10k + 4 S(k)=10k3+9k2+10k+4Use the factor theorem to show that (2k+1)(2k + 1)(2k+1) is a factor of S(k)S(k)S(k).
Express S(k)S(k)S(k) in the form
S(k)=(2k+1)(ak2+bk+c) S(k) = (2k + 1)(ak^2 + bk + c) S(k)=(2k+1)(ak2+bk+c)where aaa, b b\,b and c c\,c are integers to be determined.
Given that n n\,n is a positive integer, use your result from part (b) to determine whether 10n3+9n2+10n+410n^3 + 9n^2 + 10n + 410n3+9n2+10n+4 can ever be a prime number. Justify your answer.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions 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), matched to the AQA A Level Maths (7357) 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.
