Finding Zeros from Factored Form

Front

What are the zeros of a polynomial function?

Back

The zeros of a polynomial function are the values of x for which the function equals zero. They are the x-intercepts of the graph of the function.

Front

How do you find the zeros from a factored form of a polynomial?

Back

Front

What is the factored form of a polynomial?

Back

Front

If a polynomial has a zero at x = 3, what does this tell you about its factors?

Back

Front

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

Back

The x-intercepts (or zeros) indicate the points where the graph of the polynomial crosses the x-axis, showing the values of x for which the function equals zero.

Front

Back

Front

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

Back

The degree of a polynomial indicates the maximum number of zeros it can have. For example, a quadratic polynomial (degree 2) can have up to 2 zeros.

Front

How can you verify if a given polynomial has the correct zeros?

Back

To verify, substitute the zeros into the polynomial equation. If the result is zero, then the zeros are correct.

Front

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

Back

Front

How do you determine the multiplicity of a zero?

Back

The multiplicity of a zero is determined by the number of times its corresponding factor appears in the factored form of the polynomial.