Chapter 2 Notes BLANK.pdf - 2.1 u2013 Classifying...

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2.1 – Classifying PolynomialsLearning Target:to classify polynomials, combine like terms, multiply monomials together and multiply a monomial with a polynomial. Toolkit: Multiply powers with the same base (add the exponents) Ex: (𝑥ሻሺ𝑥ሻ ൌDefinitions: Term: a number or a product of a number with one or more variables, which can be raised to a power. Ex: Polynomial: A term or sum of terms, in which all variables have wholenumber exponents, and which variables only appear in the numerator. Ex:Examples of Polynomials Classifying Polynomials Degree of a Polynomial Leading Term The degree of a term is the sumof the exponents of the variables of that term. The degree of a polynomial is the term with the highestdegree. The term in a polynomial with the highest degree.
Combining like Terms Multiplying a monomial by a monomial Ex 1) Fill out the chart for the following polynomial: 4𝑥𝑦െ 10𝑥𝑦 ൅ 7Terms: Coefficients: Degree of each term: Leading Term: Degree of polynomial:Like termsare any terms in a polynomial that have the same variables to the same power. To combine like terms, add or subtract the coefficients. Ex 2) Like terms: Not like terms:3𝑥െ 5𝑥4𝑥𝑦 5𝑥𝑦Simplify the following expression: െ10𝑥െ 𝑦 ൅ 4𝑥൅ 7𝑦Ex 3) Step 1:Multiply the constants together. Step 2: Multiply the variables together (add exponents of variables with the same base). Multiply the following: a) ሺ2𝑥ሻሺെ3𝑥b) ሺ3𝑥𝑦ሻሺ5𝑥𝑦c) ሺെ2𝑎𝑏ሻሺ5𝑎𝑏ሻሺെ𝑎𝑏ሻ
Multiplying a polynomial by a monomial Use the Distributive Property to multiply a monomial with a polynomial: The Distributive Property:

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