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5.1 Addition and Subtraction of Polynomials and Polynomial Functions

5.1 Addition and Subtraction of Polynomials and Polynomial Functions. Concepts 1, 2, 3, and 4. 5.1.1 Polynomials: Basic Definitions. A polynomial in x is defined as a finite sum of terms in the form ax n . n is a whole number. a is a real number.

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5.1 Addition and Subtraction of Polynomials and Polynomial Functions

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  1. 5.1 Addition and Subtraction of Polynomials and Polynomial Functions Concepts 1, 2, 3, and 4

  2. 5.1.1 Polynomials: Basic Definitions • A polynomial in x is defined as a finite sum of terms in the form axn . • n is a whole number. • a is a real number. • a is called the coefficient of the term.

  3. Number of Terms • Polynomials can be named by how many terms they have. • Monomial: a polynomial with one term. • Binomial: a polynomial with two terms. • Trinomial: a polynomial with three terms.

  4. Degree • Degree of a Monomial – the sum of all the exponents. • Degree of a Polynomial – the highest degree term.

  5. 5.1.2 Addition of Polynomials • “combine like terms” • Like terms have exactly the same variables with the same powers. • Examples:

  6. 5.1.3 Subtraction of Polynomials • KEY: Distribute the negative • In other words, add the opposite • Example, what is the opposite of each polynomial?

  7. Subtract the polynomials

  8. Subtracting From • Subtract 7 from 10. • Subtract 12 from 4.

  9. 5.1.4 polynomial functions • A function defined by a polynomial YES NO

  10. Evaluating polynomial functions

  11. New homework policy • Everyday we do a new section, a few problems will be assigned. Each week (on any day) we will randomly pick one or two assignments to grade. Make sure to show your work and circle your final answer. • Your assignment for 5.1 • Pg. 316 – 318 #18, 34, 66, 72, 76, 80

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