Roots and multiplicity of a polynomial function

Front

What is the factored form of a polynomial with roots x=-2, x=5, and x=2/3?

Back

y=(x+2)(x-5)(3x-2)

Front

Which of the following is not a zero of the polynomial f(x)=-2x(3x+1)^2(x+7)^7?

Back

-2 is not a zero.

Front

What are the roots of the polynomial function y = (x + 2)(x - 7)^3?

Back

The roots are -2 and 7 with multiplicity 3.

Front

What are the zeros of the polynomial y = 3(x + 4)(x + 1)(x - 3)?

Back

The zeros are -4, -1, and 3.

Front

What does it mean for a zero to have multiplicity?

Back

Multiplicity refers to the number of times a particular root appears in the factored form of a polynomial.

Front

How do you determine the multiplicity of a root from a polynomial's factored form?

Back

The multiplicity of a root is determined by the exponent of the factor corresponding to that root.

Front

What is the relationship between the roots of a polynomial and its graph?

Back

The roots of a polynomial correspond to the x-intercepts of its graph.

Front

If a polynomial has a root of multiplicity 2, what does this imply about the graph at that root?

Back

The graph will touch the x-axis at that root but not cross it.

Front

What is the significance of a zero with multiplicity 1?

Back

A zero with multiplicity 1 indicates that the graph will cross the x-axis at that point.

Front

How can you find the zeros of a polynomial given its factored form?

Back

Set each factor equal to zero and solve for x.