5.3/4 Polynomial Zeros: Graphs

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

How many zeros can a polynomial of degree n have?

Back

A polynomial of degree n can have at most n zeros.

Front

What is the relationship between the zeros and the factors of a polynomial?

Back

The zeros of a polynomial correspond to the values of x that make each factor equal to zero.

Front

What does the graph of a polynomial function look like at its zeros?

Back

At its zeros, the graph of a polynomial function intersects the x-axis.

Front

What is the difference between real zeros and complex zeros?

Back

Real zeros are the x-intercepts of the graph, while complex zeros do not correspond to any points on the graph.

Front

How can you find the zeros of a polynomial function?

Back

You can find the zeros by factoring the polynomial or using the quadratic formula for quadratic polynomials.

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its linear factors.

Front

What does it mean if a polynomial has a repeated zero?

Back

A repeated zero indicates that the polynomial touches the x-axis at that point but does not cross it.

Front

How do you determine the multiplicity of a zero?

Back

The multiplicity of a zero is determined by the exponent of the corresponding factor in the polynomial.

Front

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

Back

The leading coefficient affects the end behavior of the polynomial's graph.