Question

Describe the end behavior of a ninth-degree polynomial with a negative leading coefficient

Answer 1

Given:

The degree of polynomial = 9

Leading coefficient is negative.

To find:

The end behavior of the polynomial.

Solution:

Let the polynomial be P(x).

We have,

Degree of polynomial = 9, which is odd.

Leading coefficient is negative.

If the degree of a polynomial is odd and leading coefficient is negative, then

$P(x)\to \infty\text{ as }x\to -\infty$

$P(x)\to -\infty\text{ as }x\to \infty$

Therefore, the end behavior of the given polynomial is $P(x)\to \infty\text{ as }x\to -\infty,P(x)\to -\infty\text{ as }x\to \infty$.