It is given that P(x)=2x3+7x2+9x+3P(x) = 2x^3 + 7x^2 + 9x + 3P(x)=2x3+7x2+9x+3
Use the factor theorem to show that (2x+1)(2x + 1)(2x+1) is a factor of P(x)P(x)P(x).
Express P(x)P(x)P(x) in the form (2x+1)(ax2+bx+c)(2x + 1)\left(ax^2 + bx + c\right)(2x+1)(ax2+bx+c), where aaa, b b\,b and c c\,c are constants to be found.
Given that n n\,n is a positive integer, use your answer to part (b) to explain why 2n3+7n2+9n+32n^3 + 7n^2 + 9n + 32n3+7n2+9n+3 is never prime.
302 exam-style questions on WJEC A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Algebra and Functions, 1.2.2 Algebra and Functions, 1.2.3 Algebra and Functions, 1.2.4 Algebra and Functions, 1.2.5 Algebra and Functions, 1.2.6 Algebra and Functions, 1.2.7 Algebra and Functions, 1.2.8 Algebra and Functions, 1.2.9 Algebra and Functions, 1.2.10 Algebra and Functions, 1.2.11 Algebra and Functions, and 1.2.12 Algebra and Functions. Each one has a worked solution and a mark scheme showing where the marks go.