10.1
Adding and Subtracting
Polynomials
Goal
Add and subtract
polynomials.
How large is the walkway around a pool?
In Example 5 you will use
subtraction of polynomials
to find the area of a walkway
around a pool.
Key Words
• monomial
• degree of a monomial
in one variable
• polynomial
• binomial
• trinomial
• standard form
• degree of a polynomial
in one variable
A monomial is a number, a variable, or the product of a number and one or more
variables with whole number exponents. The following expressions are monomials.
8
2x
3x2y
1
x2
2
The degree of a monomial is the sum of the exponents of the variables in the
monomial. The degree of 3x2 is 2. The degree of 6z4 is 4. The degree of 3x2y
is 2 1, or 3.
Student Help
READING ALGEBRA
The monomial 5x 4 is
read as “negative five
times x to the fourth
power.” The coefficient
is 5.
EXAMPLE
1
Find the Degree of a Monomial
State the degree of the monomial.
1
b. b3
2
a. 5x4
c. 12
Solution
a. The exponent of x is 4.
ANSWER 䊳
The degree of the monomial is 4.
b. The exponent of b is 3.
ANSWER 䊳
The degree of the monomial is 3.
c. Recall 12 12x0, so the exponent is 0.
ANSWER 䊳
The degree of the monomial is 0.
Find the Degree of a Monomial
State the degree of the monomial.
1. 6x3
568
Chapter 10
Polynomials and Factoring
2. 4p
3. 10
4. 3a5