Roots and multiplicity of a polynomial function

Front

What is the multiplicity of a root?

Back

It is the number of times the corresponding factor is repeated.

Front

How does a factor with multiplicity of 2 affect the graph of a polynomial function?

Back

It causes the graph to touch the x-axis and bounce off.

Front

What is the leading coefficient of a polynomial?

Back

It is the coefficient of the term with the highest degree.

Front

What does it mean if a zero has multiplicity 1?

Back

The graph crosses the x-axis at that zero.

Front

What does it mean if a zero has multiplicity 2?

Back

The graph touches the x-axis at that zero and bounces off.

Front

Back

The zeros are 0, -3 (multiplicity 2), and 2.

Front

What is the degree of a polynomial?

Back

The degree is the highest power of the variable in the polynomial.

Front

How can you determine the number of x-intercepts from the roots of a polynomial?

Back

Count the distinct roots and consider their multiplicities.

Front

What is a polynomial function?

Back

Front

What is the significance of the leading coefficient in a polynomial?

Back

It determines the end behavior of the graph of the polynomial.