Characteristics of Polynomials Mixed Review

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How do you determine the degree of a polynomial?

Back

The degree of a polynomial is determined by the highest exponent of the variable in the polynomial.

Front

What does it mean if a polynomial has an even degree?

Back

If a polynomial has an even degree, its end behavior will be the same on both ends of the graph (either both up or both down).

Front

What does it mean if a polynomial has an odd degree?

Back

If a polynomial has an odd degree, its end behavior will be opposite on both ends of the graph (one end up and the other end down).

Front

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

Back

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

Front

What is a factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its factors, which can provide insights into its roots and graph.

Front

How can you identify the roots of a polynomial from its factored form?

Back

The roots of a polynomial can be identified by setting each factor equal to zero and solving for the variable.

Front

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

Back

A polynomial of degree n can have at most n roots, counting multiplicities.

Front

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

Back

A repeated root occurs when a factor of the polynomial appears more than once, indicating that the graph touches the x-axis at that root but does not cross it.