Adding and Subtracting Polynomials

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Sharp Tutor Fri, Jan 14, 2022 11:44 PM UTC

OBJECTIVES:
1. Know the basic definitions for polynomials. 2. Find the degree of a polynomial. 3. Add and subtract polynomials

1. Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 6.2 - 1

2. Chapter 6
Exponents, Polynomials, and
Polynomial Functions
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 6.2 - 2

3. 6.2
Adding and Subtracting
Polynomials
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 6.2 - 3

4. 6.2 Adding and Subtracting Polynomials
Objectives
1. Know the basic definitions for
polynomials.
2. Find the degree of a polynomial.
3. Add and subtract polynomials.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.2 - 4

5. 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. Sec 6.2 - 5

6. 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. Sec 6.2 - 6

7. 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. Sec 6.2 - 7

8. 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. Sec 6.2 - 8

9. 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. Sec 6.2 - 9

10. 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. Sec 6.2 - 10

13. 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. Sec 6.2 - 13

14. 6.2 Adding and Subtracting Polynomials
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. Sec 6.2 - 14

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