Exponents, Polynomials, and Polynomial Functions Chapter 6 Exponents, Polynomials, and Polynomial Functions

Adding and Subtracting Polynomials 6.2 Adding and Subtracting Polynomials

6.2 Adding and Subtracting Polynomials Objectives Know the basic definitions for polynomials. Find the degree of a polynomial. Add and subtract polynomials. Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.2 Adding and Subtracting Polynomials Know the basic definitions for polynomials. Polynomials are fundamental in algebra. Recall from Section 1.4 that a term is a number, a variable, or the product or quotient of a number of one or more variables raised to powers. Examples of terms include: Coefficients are written in blue. Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.2 Adding and Subtracting Polynomials Know the basic definitions for polynomials. Recall that any combination of variables or constants (numerical values) joined by the basic operations of addition, subtraction, multiplication, and division (except by 0), or raising to powers or taking roots is called an algebraic expression. Polynomials are the simplest kind of algebraic expression. Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.2 Adding and Subtracting Polynomials Know the basic definitions for polynomials. A polynomial containing only the variable x is called a polynomial in x. A polynomial in one variable is written in descending powers of the variable if the exponents on the variable decrease from left to right. The powers of x are decreasing from left to right. We can think of this polynomial as Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.2 Adding and Subtracting Polynomials Some Common Polynomials Polynomials having a specific number of terms are commonly given special names. Trinomial = a polynomial with three terms Binomial = a polynomial with two terms Monomial = a polynomial with one term Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.2 Adding and Subtracting Polynomials The Degree of a Polynomial The degree of a nonzero term with only one variable is the exponent on the variable. The number 0 has no degree. The degree of a polynomial is the highest degree of any of its nonzero terms. Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.2 Adding and Subtracting Polynomials Addition and Subtraction of Polynomials Addition of polynomials is just a matter of adding up like terms. For example, consider the following polynomials: We can use the associative and commutative properties to rearrange the terms and then we add the like terms. Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.2 Adding and Subtracting Polynomials Adding Polynomials Perform the addition in each case: Vertical Solution Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.2 Adding and Subtracting Polynomials Subtraction of Polynomials Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.2 Adding and Subtracting Polynomials Subtraction of Polynomials To subtract B from A, we add the negative of B to A. Perform the indicated subtractions. Copyright © 2010 Pearson Education, Inc. All rights reserved.

6.2 Adding and Subtracting Polynomials We can subtract these polynomials vertically by writing the first polynomial above the second, lining up like terms in columns. Change all the signs in the second polynomial, and add. Copyright © 2010 Pearson Education, Inc. All rights reserved.