Multiplicity PreAP

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 multiplicity mean in relation to zeros?

Back

Multiplicity refers to the number of times a particular zero is repeated in a polynomial.

Front

If a polynomial has a zero with multiplicity 1, how does it behave at that zero?

Back

The graph of the polynomial crosses the x-axis at that zero.

Front

If a polynomial has a zero with multiplicity 2, how does it behave at that zero?

Back

The graph of the polynomial touches the x-axis at that zero but does not cross it.

Front

What are the zeros of the polynomial y = 3x(x - 6)(x + 5)?

Back

The zeros are 0, 6, and -5.

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 degree of a polynomial?

Back

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

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree.

Front

What does it mean for a function to cross the x-axis?

Back

It means that the function has a zero at that point.

Front

What does it mean for a function to be tangent to the x-axis?

Back

It means that the function touches the x-axis at that point but does not cross it.