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**Polynomials Identify Monomials and their Degree**

Identify Polynomials and their Degree Adding, Subtracting, Multiplying, and Dividing Polynomial Expressions

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**The degree of a monomial is the sum of the exponents of the variables.**

A monomial is the product of a constant times a variable raised to a nonnegative integer power. The degree of a monomial is the sum of the exponents of the variables. A polynomial is a monomial or the sum of monomials. The degree of a polynomial is the monomial with the highest degree.

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**Variables with negative exponents**

Polynomials cannot have the following: Variables with negative exponents Variable exponents Variables under the radical sign

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**State the coefficient and the degree of each polynomial**

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**Adding and Subtracting Polynomials**

Change (-) to (+) of the opposite Use the Distributive Property Combine all like terms Write your answer in standard form

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**Simplify Each Expression**

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**Multiplying Polynomials**

Follow all rules for exponents FOIL Method for multiplying binomials Use Distributive Property for all others Use special products when applicable Combine all like terms Write your answer in standard form

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Rule: Square 2x the product

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**Squaring A Trinomial Square each term and 2x each product**

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**Perform the indicated operation below and express as a single polynomial**

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**Perform the indicated operation below and express as a single polynomial**

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**Perform the indicated operation below and express as a single polynomial**

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**Monomial Division Divide each term by the Monomial**

Follow your rules for exponents

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Polynomial Division List all of the terms with their powers in descending order Replace any missing terms with a zero Divide the polynomial until the degree of the divisor is greater than the degree of the remainder Write the remainder over the divisor

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**Perform the indicated operation below**

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Synthetic Division List all of the terms with their powers in descending order Replace missing terms with a coefficient of 0 List all of the coefficients in descending order Set the divisor equal to zero and solve Write your final answer using the coefficients as one power less than the original polynomial Write the remainder over the divisor

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**Perform the indicated operation below**

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Section R3: Polynomials

Section R3: Polynomials

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