Polynomial Graphs

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 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 typically results in the graph having the same end behavior on both sides.

Front

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

Back

A polynomial has an odd degree if the highest exponent of its variable is an odd number, which typically results in the graph having opposite end behavior on both sides.

Front

How do you determine the leading coefficient of a polynomial?

Back

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

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: 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 a zero of a polynomial?

Back

A zero of a polynomial is a value of the variable that makes the polynomial equal to zero.

Front

What is the multiplicity of a zero?

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The multiplicity of a zero refers to the number of times a particular zero is repeated in the polynomial's factorization.

Front

How do you find the polynomial given its zeros and their multiplicities?

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To find the polynomial, multiply the factors corresponding to each zero raised to the power of its multiplicity.

Front

What is the general form of a polynomial?

Back

Front

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

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