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
[tex]f(x)=x-x^5[/tex]
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
[tex]f(x)=(x^2-1)(x^3+x-3)[/tex]
When we multiply the 2 brackets we will find the greatest power of x will be 5
[tex]\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}[/tex]
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
