1.2.8 Algebra and Functions

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 $V (t)$ .

[2]

Factorise $V (t)$ completely.

[3]

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

[3]

1.2.8 Algebra and Functions Questions

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 $V (t)$ .

[2]

Factorise $V (t)$ completely.

[3]

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

[3]