Zeros of Polynomials

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

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for x.

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 for a polynomial to be in factored form?

Back

A polynomial is in factored form when it is expressed as a product of its factors, such as (x - a)(x - b).

Front

If a polynomial has a zero at x = 3, what does this imply?

Back

It implies that (x - 3) is a factor of the polynomial.

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 is the significance of the zeros of a polynomial in graphing?

Back

The zeros of a polynomial indicate the x-intercepts of the graph of the polynomial.

Front

How can you verify if a number is a zero of a polynomial?

Back

Substitute the number into the polynomial; if the result is zero, it is a zero.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is f(c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of f(x) if and only if f(c) = 0.