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1 Unit 1: Pure Mathematics A

It is given that $P(x) = 2x^3 + 7x^2 + 9x + 3$

Use the factor theorem to show that $(2 x + 1)$ 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 $2n^3 + 7n^2 + 9n + 3$ is never prime.

[2]

1 Unit 1: Pure Mathematics A Questions

It is given that $P(x) = 2x^3 + 7x^2 + 9x + 3$

Use the factor theorem to show that $(2 x + 1)$ 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 $2n^3 + 7n^2 + 9n + 3$ is never prime.

[2]