Question

In Problems 15–26, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell

why not.

$Q\left(x\right)=-3x^2{(x+2)}^3$

Short answer

$G$ is a polynomial function of degree$5$

Step-by-step solution

Given information

$Q\left(x\right)=-3x^2{(x+2)}^3$

Calculation

$$\begin{gathered} Q\left(x\right)=-3x^2{(x+2)}^3 \\ =-3x^2(x^3+2^3+3.x^2.2+3.x.2^2) \\ =-3x^2(x^3+8+6x^2+12x) \\ =-3x^5-24x^2-18x^4-36x^3 \end{gathered}$$

$G$is a polynomial function of degree $5$