Question

Which of the following are fifth degree polynomial functions? Select all that apply.2 answers

Answer 1

The greatest power of the polynomial function is its degree

Since we need the 5th degree, then the greatest power of x must be 5

From the given figure, we can see that the function in answer A is

`f(x)=x-x^5`

The function has the greatest power of x = 5, then

This function in answer A is in the 5th degree

The function in answer D is

`f(x)=(x^2-1)(x^3+x-3)`

When we multiply the 2 brackets we will find the greatest power of x will be 5

`\begin{gathered} f(x)=x^2(x^3)+x^2(x)+x^2(-3)-1(x^3)-1(x)-1(-3) \\ f(x)=x^5+x^3-3x^2-x^3-x+3 \end{gathered}`

Since the greatest power of x is 5, then

The function in answer D is in the 5th degree

The answers are A and D