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 $E (t)$ .

Factorise $E (t)$ completely.

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

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 $E (t)$ .

Factorise $E (t)$ completely.

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

1.1 Algebra and functions

1.1 Algebra and functions Questions