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

Question

asked Jun 6, 2019 220k views

2 Answers

Vpozdyayev · Answer 1 · 2019-06-12T08:41:59+0000

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.