Q. 25 - Precalculus Enhanced with Graphing Utilities

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.

$G\left(x\right)=2{(x-1)}^2(x^2+1)$

Step-by-Step Solution

Answer

$G$is a polynomial function of degree $4$ .

Step 1: Given information

$G\left(x\right)=2{(x-1)}^2(x^2+1)$

Step 2: Calculation

$$\begin{gathered} G\left(x\right)=2{(x-1)}^2(x^2+1) \\ =2(x^2-2x+1)(x^2+1) \\ =2\left\{x^2\right(x^2-2x+1)+1(x^2-2x+1\left)\right\} \\ =2\left\{\right(x^4-2x^3+x^2)+x^2-2x+1\} \\ =2(x^4-2x^3+2x^2-2x+1) \\ =2x^4-4x^3+4x^2-4x+2 \end{gathered}$$

$G$is a polynomial function of degree $4$