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1.5.6 Polynomials and rational expressions

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Question 9

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

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

[2]

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

[2]

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.

[2]

Markscheme

1.5.6 Polynomials and rational expressions Questions

A Level
Maths
1.5.6 Polynomials and rational expressions

113 exam-style questions on AQA A Level Maths 1.5.6 Polynomials and rational expressions. Each one has a worked solution and a mark scheme showing where the marks go.

1.5.6 Polynomials and rational expressions

Question bank

1.5.6 Polynomials and rational expressions

Easy Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12

Question 9

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

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

[2]

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

[2]

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.

[2]

Markscheme

1.5.6 Polynomials and rational expressions Questions

A Level
Maths
1.5.6 Polynomials and rational expressions

113 exam-style questions on AQA A Level Maths 1.5.6 Polynomials and rational expressions. Each one has a worked solution and a mark scheme showing where the marks go.