Finding Zeros of Polynomials Flashcard Review (Quiz Review)

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero. It is also known as a root or solution of the polynomial.

Front

State the Fundamental Theorem of Algebra.

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial equation of degree n has exactly n complex roots, counting multiplicities.

Front

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

Back

To find the zeros of a polynomial in factored form, set each factor equal to zero and solve for x.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

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

Back

The number of zeros of a polynomial is equal to its degree, considering multiplicities.

Front

What does it mean for a polynomial to have a repeated root?

Back

A repeated root is a root that occurs more than once in the polynomial, which affects the graph's behavior at that point.

Front

How can you determine the number of real zeros of a polynomial?

Back

You can determine the number of real zeros by analyzing the polynomial's graph or using the Descartes' Rule of Signs.

Front

What is synthetic division and how is it used in finding zeros?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor, helping to find zeros.

Front

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

Back

The x-intercepts of a polynomial function represent the zeros of the polynomial, where the graph crosses the x-axis.

Front

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

Back

To verify if a number is a zero, substitute it into the polynomial and check if the result equals zero.