How to Find the Multiplicity from a Set of Polynomial Factors

The video tutorial explains how to find zeros of a polynomial and determine their multiplicity. It begins with an introduction to zeros and the zero product property, followed by solving polynomial equations using inverse operations. The concept of multiplicity is introduced, explaining how it affects the graph of a polynomial. The tutorial concludes with a discussion on the significance of even and odd multiplicities in graph behavior.

What does the Zero Product Property state?

• If a product of terms equals zero, none of the terms can be zero.

• If a product of terms equals zero, all terms must be zero.

• If a product of terms equals zero, at least one term must be zero.

• If a product of terms equals zero, the terms are all positive.

How do you find the zeros of a polynomial?

• By setting each factor of the polynomial equal to one.

• By setting each factor of the polynomial equal to zero.

• By setting the polynomial equal to one.

• By setting the polynomial equal to infinity.

What is the multiplicity of a zero?

• The number of terms in the polynomial.

• The power to which a factor is raised.

• The number of factors in the polynomial.

• The number of times a zero appears in the polynomial.

If a factor in a polynomial is raised to the power of 3, what is the multiplicity of the corresponding zero?

• 3

• 4

• 2

• 1

What does an even multiplicity indicate about the graph at a zero?

• The graph remains constant at the zero.

• The graph crosses the zero.

• The graph has a vertical asymptote at the zero.

• The graph touches and bounces back at the zero.

What happens to the graph at a zero with an odd multiplicity?

• The graph touches and bounces back at the zero.

• The graph crosses the zero.

• The graph has a vertical asymptote at the zero.

• The graph remains constant at the zero.

Why is understanding multiplicity important in graphing polynomials?

• It determines the degree of the polynomial.

• It alters the domain of the polynomial.

• It changes the leading coefficient of the polynomial.

• It affects how the graph behaves at each zero.