Polynomial Functions

Front

What is a polynomial?

Back

Front

What is the degree of a polynomial?

Back

Front

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

Back

A polynomial has an even degree if the highest power of the variable is an even number. Even degree polynomials have the same end behavior on both sides of the graph.

Front

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

Back

A polynomial has an odd degree if the highest power of the variable is an odd number. Odd degree polynomials have opposite end behavior on both sides of the graph.

Front

What is a leading coefficient?

Back

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 the variable. The solutions are the x-values where the graph intersects the x-axis.

Front

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

Back

The sign of the leading coefficient affects the end behavior of the polynomial. A positive leading coefficient means the graph rises to the right, while a negative leading coefficient means it falls to the right.

Front

What is the difference between a polynomial and a monomial?

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A polynomial is a sum of one or more monomials. A monomial is a single term that can be a constant, a variable, or a product of constants and variables.

Front

What is the standard form of a polynomial?

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

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The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n zeros, counting multiplicities, in the complex number system.