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1 Unit 1: Pure Mathematics A

A theoretical model for the potential energy $E$ in a micro-system is given by the function

E(t) = 27t^3 + 54t^2 + 33t + 6

where $t$ is a dimensionless time parameter.

Use the factor theorem to prove that $(3 t + 1)$ is a factor of $E (t)$ .

[2]

Factorise $E (t)$ completely.

[3]

Hence, prove that $108n^3 + 216n^2 + 132n + 24$ is a multiple of 24 when $n$ is a positive integer.

[3]

1 Unit 1: Pure Mathematics A Questions

A theoretical model for the potential energy $E$ in a micro-system is given by the function

E(t) = 27t^3 + 54t^2 + 33t + 6

where $t$ is a dimensionless time parameter.

Use the factor theorem to prove that $(3 t + 1)$ is a factor of $E (t)$ .

[2]

Factorise $E (t)$ completely.

[3]

Hence, prove that $108n^3 + 216n^2 + 132n + 24$ is a multiple of 24 when $n$ is a positive integer.

[3]