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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 63

It is given that $P(x) = 3x^3 + 4x^2 + 4x + 1$

a.

Use the factor theorem to show that $(3 x + 1)$ is a factor of $P (x)$ .

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b.

Express $P (x)$ in the form $1)\left(ax^2 + bx + c\right)$ , where $a$ , $b\,$ and $c\,$ are constants to be found.

[2]

c.

Given that $n\,$ is a positive integer, use your answer to part (b) to explain why $3n^3 + 4n^2 + 4n + 1$ is never prime.

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Markscheme

1.5 B: Algebra and functions Questions

A Level
Maths
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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