Zeros from Factored Form

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x that make the polynomial equal to zero.

Front

In the equation (x + 2)(x - 3) = 0, what are the factors?

Back

The factors are (x + 2) and (x - 3).

Front

How do you find the zeros from factored form?

Back

Set each factor equal to zero and solve for x.

Front

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

Back

A polynomial of degree n can have up to n zeros.

Front

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

Back

A repeated factor indicates that the corresponding zero has a multiplicity greater than one.

Front

How many zeros does the polynomial function P(x) = 3x^4 + 4x - 8 have?

Back

It has 4 zeros.

Front

List the zeros for the function f(x)=(x+4)(x-3)(x-2).

Back

The zeros are -4, 3, and 2.

Front

What is the factored form of a polynomial?

Back

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

Front

If f(x) = (x-4)(x-1)^2(x+2), what are the zeros?

Back

The zeros are 4, 1 (with multiplicity 2), and -2.

Front

What is the significance of the x-intercepts of a polynomial graph?

Back

The x-intercepts correspond to the zeros of the polynomial.