Zeros and Multiplicity of Polynomials

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.

Front

What does the multiplicity of a zero indicate?

Back

The multiplicity of a zero indicates how many times that zero is repeated in the polynomial and affects the behavior of the graph at that zero.

Front

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

Back

The graph crosses the x-axis at that zero.

Front

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

Back

The graph touches the x-axis and turns around at that zero.

Front

If a polynomial has a zero at x = 2 with multiplicity 3, what does this mean?

Back

It means that (x - 2) is a factor of the polynomial raised to the power of 3, and the graph will cross the x-axis at x = 2.

Front

How can you determine the multiplicity of a zero from a polynomial's factored form?

Back

The multiplicity is determined by the exponent of the factor corresponding to that zero.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have up to n zeros, counting multiplicities.

Front

What is the significance of a zero with multiplicity 1?

Back

A zero with multiplicity 1 indicates that the graph will cross the x-axis at that point.

Front

What is the significance of a zero with multiplicity greater than 1?

Back

A zero with multiplicity greater than 1 indicates that the graph will touch the x-axis and turn around at that point.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros, set the polynomial equal to zero and solve for x.