An engineer determines that the volume $V (t)$ of a specialized industrial component is modeled by the polynomial:

V(t) = 125t^3 + 150t^2 + 55t + 6

where $t\,$ is a dimension-scaling factor.

Use the factor theorem to prove that $(5 t + 1)$ is a factor of $V (t)$ .

Factorise $V (t)$ completely.

Hence, prove that $375m^3 + 450m^2 + 165m + 18$ is a multiple of 18 when $m\,$ is a positive whole number.

An engineer determines that the volume $V (t)$ of a specialized industrial component is modeled by the polynomial:

V(t) = 125t^3 + 150t^2 + 55t + 6

where $t\,$ is a dimension-scaling factor.

Use the factor theorem to prove that $(5 t + 1)$ is a factor of $V (t)$ .

Factorise $V (t)$ completely.

Hence, prove that $375m^3 + 450m^2 + 165m + 18$ is a multiple of 18 when $m\,$ is a positive whole number.

1.1 Algebra and functions

1.1 Algebra and functions Questions