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MTH 091 Section 10.3 Introduction to Polynomials Section 10.4 Adding and Subtracting Polynomials

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What Is A Polynomial? A polynomial is an algebraic expression with “counting number” exponents on. Parts of a polynomial: 1.Variables 2.Constants 3.Coefficients Terms are separated by addition and subtraction signs. Polynomials can be classified by type. One term = monomial Two terms = binomial Three terms = trinomial More than three terms = polynomial

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More About Polynomials Polynomials can also be classified by degree. The degree is the largest exponent on any term. If the terms have more than one variable, add the exponents on each term to get the degree of that term. A polynomial written in descending order has the terms arranged from greatest exponent to least exponent.

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For the polynomial -6x 6 +4x 5 +7x 3 -9x 2 -1, complete the chart below: TermCoefficientDegree 7x 3 -9 6 4

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Evaluating A Polynomial Evaluating a polynomial is the same as evaluating an algebraic expression (substitute and simplify). Recall that the order of operations requires that we perform exponents before we perform multiplication.

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Examples Find the degree and type of each polynomial: -6y + 4 a + 5a 2 + 3a 3 – 4a 4 7r 2 + 2r – 3r 5 Evaluate each polynomial for x = -1: x 2 + 3x – 4 -2x 3 + 3x 2 – 6

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Adding Polynomials: Like Terms Revisited Recall that like terms will have the same variables, with the same exponents on those variables. When we add or subtract like terms, we add or subtract the coefficients only. DO NOT add the exponents!

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Subtracting Polynomials Apply “Keep-Change-Change” 1.Keep the first polynomial. 2.Change the subtraction sign between polynomials to an addition sign. 3.Change the signs of all the terms in the second polynomial. 4.Add.

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Add or Subtract as Indicated

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