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The Vocabulary of (in one variable) Word & Definition  : A fixed real  Variable: A letter used to represent a changeable number  : A constant standing alone or a constant multiplied by a variable raised to a whole number power  : A single term  : A sum of two terms that cannot be combined  Trinomial: A sum of three terms that cannot be combined  : A sum of any number of terms  : The constant number factor of a term  Degree (of a term): The whole number exponent on the variable in a term  Degree (of the polynomial): The greatest degree of any term in the polynomial Combining Like Terms Polynomial terms can only be added when they are “like terms”: they have the same variable raised to the same power. Consider these pairs of terms. Terms & Like or Unlike?

 8푥2, 5푥2 : Like terms; the variable 푥 is raised to the second power in both

 9푦3, 4푦 : Unlike terms; the variable 푦 has different powers

 −23푥, 7푦 : Unlike terms; the variable 푦 has different powers

3  푧5, −6.5푧5 : Like terms; the variable 푧 is raised to the fifth power in both 4

To combine like terms, add the . Keep the exponent on the variable the same as in each of the original terms. For example

 8푥2 + 5푥2 = (8 + 5)푥2 = 13푥2

3 3 1  푧5 − 푧5 = ( − 1) 푧5 = − 푧5 4 4 4

For more practice, see Add and Subtract Polynomials. Then answer the following questions.

1. What is the degree of the polynomial 4푦5 − 2푦7 + 8푦?

3 2 3 2 2. Add (푥 + 7푥 − 5푥 − 16) + (4푥 − 3푥 − 7푥 + 13)

The link included here will take the reader to OpenStax Elementary , which is published under a Creative Commons Attribution License 4.0. Download for free at http://cnx.org/contents/[email protected]

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