Question

What are the possible degrees for the polynomial function?

degrees of 6 or greater
even degrees of 6 or greater
degrees of 5 or greater
odd degrees of 5 or greater

Answer 1

Even degrees of six or greater

Answer 2

Answer: Even degrees of 6 or greater

Explanation:

Degree of a polynomial is the highest power of its term (monomial) having non-zero coefficients.

Also, the degree is even or odd shows the end behavior of the polynomial and the value of the degree shows the maximum number of roots.(x-intercepts)

When we see the given diagram, we found that the function has at least 6 roots,

Thus, it has degree of 6 or more than 6.

Now, the end behavior of the given graph is,

`f(x)\rightarrow -\infty` as
`x\rightarrow \infty`

`f(x)\rightarrow -\infty` as
`x\rightarrow -\infty`

Which is the end behavior of an even function,

⇒ Given polynomial has even degree.

⇒ Second option is correct.