When a polynomial is written in factored form, we can identify several facts about it.

For example, the factored form of the polynomial shown in the graph is .

Graph of a polynomial, xy-axis. Horizontal and vertical axis, both scale -5 to 4, by 1’s. Graph is increasing from left from near (-2 comma -5), passes through (-1 comma 0) and (0 comma 3) as a maximum with a smooth curve. Graph is decreasing from (0 comma 3), passes though (2 comma 0) to a minimum at about (2 point 5 comma -0 point 5) with a smooth curve, and then increasing, passes through (3 comma 0) and keeps increasing up through about (4 comma 4) and beyond.

The graph has -intercepts at 3, 2, and -1. Each of these -values makes one of the factors in the expression equal to 0, and so makes the equation true. The numbers 3, 2, and -1 are known as the zeros of the function.

When a polynomial is not written in factored form, identifying the zeros from the expression for the polynomial can be more challenging. We’ll learn how to do that in future lessons.