Multiplicity

Front

What are the zeros of the polynomial function y = x(x - 6)(x + 5)?

Back

0, 6, -5

Front

What effect do odd multiplicities have on the x-axis?

Back

They cause the graph to cross the x-axis.

Front

If the graph of a function crosses the x-axis, what does that indicate about the multiplicity of that zero?

Back

It indicates that the multiplicity is odd.

Front

What are the zeros of the function y = (x + 2)(x - 3)(3x - 5)?

Back

x = -2, x = 3, x = 5/3

Front

What is the definition of a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x that makes the function equal to zero.

Front

How do you find the zeros of a polynomial function?

Back

Set the polynomial equal to zero and solve for x.

Front

What is the significance of even multiplicities on the x-axis?

Back

Even multiplicities cause the graph to touch the x-axis but not cross it.

Front

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

Back

The degree of a polynomial indicates the maximum number of zeros it can have.

Front

What does it mean if a polynomial has a zero with a multiplicity of 2?

Back

It means that the zero is repeated and the graph will touch the x-axis at that point without crossing it.

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.