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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.1 Adding and Subtracting Polynomials Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1

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3 Polynomials A polynomial is a single term or the sum of two or more terms containing variables with whole number exponents. Consider the polynomial: This polynomial contains four terms. It is customary to write the terms in order of descending powers of the variable. This is the standard form of a polynomial. Here are two other polynomials which are written in standard form.

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 4 The Degree of ax n If a ≠ 0, the degree of ax n is n. The degree of a nonzero constant term is 0. The constant 0 has no defined degree. Degree 3 Degree 2 Degree 1 Degree of nonzero constant: 0 Polynomials

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 5 The degree of a polynomial is the degree of its highest order term. Example: Degree 3 Polynomial: Degree 4 Polynomial: Degree of a Polynomial

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 6 Monomial: A polynomial with one term. Binomial: A polynomial with two terms. Trinomial: A polynomial with three terms. Example: This is a 4 th degree trinomial. Special Polynomials

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 7 Objective #1: Example

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 8 Objective #1: Example

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 9

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10 Polynomials Adding Polynomials Polynomials are added by removing the parentheses that surround each polynomial (if any) and then combining like terms.

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 11 Polynomials are added by combining like terms. Like terms are terms containing exactly the same variables to the same powers. Example : These like terms both contain x to the second power. Add the coefficients and keep the same variable factor. Adding Polynomials

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 12 Adding PolynomialsEXAMPLE SOLUTION Add: Remove parentheses Rearrange terms so that like terms are adjacent Combine like terms

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 13 Objective #2: Example

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 14 Objective #2: Example

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 15 Objective #2: Example

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 16 Objective #2: Example

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 17

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 18 Polynomials Subtracting Polynomials To subtract two polynomials, add the first polynomial and the opposite of the polynomial being subtracted.

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 19 Objective #3: Example

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 20 Objective #3: Example

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 21 Objective #3: Example

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 22 Objective #3: Example

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 23

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 24 Graphs of Polynomial Functions Graphs of equations defined by polynomials of degree 2, such as have a mirror like quality. We can obtain their graphs, shaped like bowls or inverted bowls, using the point- plotting method for graphing an equation in two variables.

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 25 Objective #4: Example

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 26 Objective #4: Example

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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 27 Objective #4: Example CONTINUED

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