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

3. Adding and Subtracting Polynomials
6.2
Adding and Subtracting Polynomials

4. 6.2 Adding and Subtracting Polynomials
Objectives
Know the basic definitions for polynomials.
Find the degree of a polynomial.
Add and subtract polynomials.
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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.
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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.
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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
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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
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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.
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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.
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11. 6.2 Adding and Subtracting Polynomials
Adding Polynomials
Perform the addition in each case:
Vertical Solution
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12. 6.2 Adding and Subtracting Polynomials
Subtraction of Polynomials
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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.
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14. 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.
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