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

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

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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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**Degree of nonzero constant: 0**

Polynomials The Degree of axn If a ≠ 0, the degree of axn is n. The degree of a nonzero constant term is 0. The constant 0 has no defined degree. Degree of nonzero constant: 0 Degree 2 Degree 1 Degree 3

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**Degree of a Polynomial Degree 3 Polynomial: Degree 4 Polynomial:**

The degree of a polynomial is the degree of its highest order term. Example: Degree 3 Polynomial: Degree 4 Polynomial:

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**Special Polynomials Monomial: A polynomial with one term.**

Binomial: A polynomial with two terms. Trinomial: A polynomial with three terms. Example: This is a 4th degree trinomial.

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Objective #1: Example

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Objective #1: Example

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**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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**Adding Polynomials 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.

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**Adding Polynomials Add: Remove parentheses**

EXAMPLE Add: SOLUTION Remove parentheses Rearrange terms so that like terms are adjacent Combine like terms

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Objective #2: Example

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Objective #2: Example

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Objective #2: Example

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Objective #2: Example

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**Subtracting Polynomials**

To subtract two polynomials, add the first polynomial and the opposite of the polynomial being subtracted.

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Objective #3: Example

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Objective #3: Example

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Objective #3: Example

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Objective #3: Example

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**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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Objective #4: Example

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Objective #4: Example

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Objective #4: Example CONTINUED

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Sect. 5.1 Polynomials and Polynomial Functions

Sect. 5.1 Polynomials and Polynomial Functions

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