Zeroes and Multiplicity of Polynomial Equations

Front

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

Back

Touches and bounces back.

Front

Identify the zeros of the polynomial f(x) = (x+2)(x-3)²(x-4).

Back

-2, 3 (multiplicity 2), 4.

Front

What is the equation in factored form of the graph that has zeros at -4, -1 (multiplicity 2), and 2?

Back

f(x) = (x+4)(x+1)²(x-2).

Front

What is the degree of the polynomial f(x) = x³(x + 3)²(x – 5)?

Back

Degree: 6.

Front

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

Back

0, 6, -5.

Front

Define 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

What is the significance of odd multiplicities at zeros?

Back

Odd multiplicities cross the x-axis.

Front

How do you determine the degree of a polynomial in factored form?

Back

Add the exponents of each factor.

Front

What does it mean if a polynomial has a zero with multiplicity greater than 1?

Back

The graph will touch the x-axis at that zero and not cross it.

Front

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

Back

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