Question

Consider the graph of the polynomial function below.

-The degree of the polynomial is... even or odd
- The leading coefficient is... negative or positive
- The polynomial has... three zeros or four zeros

Answer 1

1. The degree of the polynomial is even.
2. The leading coefficient is positive.
3. The polynomial has four zeros.

Explanation:

As shown at the graph

The polynomial function intersects with x-axis at 4 points and opens up.

So, we can deduce that:

1) The degree of the polynomial is the fourth degree because it have 4 points of intersection with the x-axis

So, The degree of the polynomial is even

2) As the curve opens up ⇒ The leading coefficient is positive

Leading coefficients are the numbers written in front of the variable with the largest exponent.

3) The polynomial has four zeros because it have 4 points of intersection with the x-axis

The zeros of the polynomial are the values of x at which y = 0