Polynomial Practice

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its factors, which can include linear factors and irreducible polynomials.

Front

What does it mean for a polynomial to have an even degree?

Back

A polynomial has an even degree if the highest exponent of its variable is an even number, which affects its end behavior.

Front

What is a leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial, determining the polynomial's end behavior.

Front

How do you determine the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x that make the polynomial equal to zero, found by solving the equation.

Front

What is standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, from highest to lowest.

Front

What is the significance of the leading coefficient's sign?

Back

The sign of the leading coefficient indicates the end behavior of the polynomial: positive means it rises to the right, negative means it falls to the right.

Front

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

Back

A polynomial of degree n can have up to n real zeros, according to the Fundamental Theorem of Algebra.

Front

What does it mean for a polynomial to be positive or negative?

Back

A polynomial is positive if its value is greater than zero for a given x, and negative if its value is less than zero.

Front

How can you identify the multiplicity of a zero?

Back

The multiplicity of a zero refers to the number of times a factor is repeated in the polynomial's factored form.

Front

What is the end behavior of a polynomial with an even degree and a positive leading coefficient?

Back

The ends of the graph will rise in both directions.