Determine the Multiplicity & Zeros of a Polynomial by Inspection

The video tutorial explains how to find the zeros of a polynomial and determine their multiplicity. It begins by defining zeros and setting the polynomial equal to zero. The zero product property is applied to find the zeros, and equations are solved to determine specific values. The concept of multiplicity is introduced, explaining how it affects the graph of the polynomial. Odd multiplicity results in the graph crossing the x-axis, while even multiplicity causes it to touch the axis. The tutorial concludes with tips on factorization and understanding multiplicity.

What is the first step in finding the zeros of a polynomial using the zero product property?

• Factor the polynomial completely

• Set the polynomial equal to 1

• Set each factor equal to zero

• Multiply all factors together

In the example problem, which of the following is a zero of the polynomial?

• X = 0

• X = 3

• X = -7

• X = 2

What does an odd multiplicity indicate about the behavior of a graph at a zero?

• The graph crosses the x-axis

• The graph remains below the x-axis

• The graph touches the x-axis

• The graph remains above the x-axis

What happens to the graph of a polynomial at a zero with even multiplicity?

• It disappears

• It remains constant

• It touches the x-axis and turns around

• It crosses the x-axis

Why is it important to write a polynomial in its factored form when finding zeros?

• It changes the polynomial's degree

• It makes the polynomial longer

• It simplifies the process of finding zeros

• It eliminates the need for graphing