Zeros and Multiplicity

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero. It is also known as a root.

Front

What does multiplicity mean in the context of polynomial zeros?

Back

Multiplicity refers to the number of times a particular zero is repeated in a polynomial. For example, if (x - 2) appears twice in the factorization, the zero 2 has a multiplicity of 2.

Front

How does a zero with odd multiplicity affect the graph of a polynomial?

Back

A zero with odd multiplicity will cross the x-axis at that zero.

Front

How does a zero with even multiplicity affect the graph of a polynomial?

Back

A zero with even multiplicity will touch the x-axis but not cross it, creating a bounce effect.

Front

What is the effect of a zero with multiplicity 1 on the graph?

Back

A zero with multiplicity 1 causes the graph to cross the x-axis.

Front

What is the effect of a zero with multiplicity 2 on the graph?

Back

A zero with multiplicity 2 causes the graph to bounce off the x-axis.

Front

What is the effect of a zero with multiplicity 3 on the graph?

Back

A zero with multiplicity 3 causes the graph to wiggle or change direction at the x-axis.

Front

Write a polynomial function with zeros at -1, 2, and 7, all with multiplicity 1.

Back

Front

Write a polynomial function with a zero at 5 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4).

Back

Front

What is the general form of a polynomial function with a zero at x = a with multiplicity m?

Back