1. EXAMPLE 1
Rewrite a polynomial
Write 15x – x3 + 3 so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial.
SOLUTION
Consider the degree of each of the polynomial’s terms.
15x – x3 + 3
The polynomial can be written as – x The greatest degree is 3, so the degree of the polynomial is 3, and the leading coefficient is –1.

2. Identify and classify polynomials
EXAMPLE 2
Identify and classify polynomials
Tell whether is a polynomial. If it is a polynomial, find its degree and classify it by the number of its terms. Otherwise, tell why it is not a polynomial.
5th degree binomial
Yes
7bc3 + 4b4c
No; variable exponent
n– 2 – 3
6n4 – 8n
2nd degree trinomial
2x2 + x – 5
0 degree monomial 9
Classify by degree and number of terms
Is it a polynomial?
Expression a. b. c. d. e.

3. EXAMPLE 3
Add polynomials
Find the sum.
a. (2x3 – 5x2 + x) + (2x2 + x3 – 1)
b. (3x2 + x – 6) + (x2 + 4x + 10)

4. EXAMPLE 3
Add polynomials
SOLUTION
a. Vertical format: Align like terms in vertical columns.
(2x3 – 5x2 + x)
+ x3 + 2x – 1
3x3 – 3x2 + x – 1
b. Horizontal format: Group like terms and simplify.
(3x2 + x – 6) + (x2 + 4x + 10) =
(3x2 + x2) + (x + 4x) + (– )
= 4x2 + 5x + 4

5. EXAMPLE 1
GUIDED PRACTICE
Rewrite a polynomial
for Examples 1,2, and 3
Write 5y – 2y2 + 9 so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial. 1.
– 2y2 +5y + 9 Degree: 2, Leading Coefficient: –2
ANSWER
Tell whether y3 – 4y + 3 is a polynomial. If it is a polynomial, find its degree and classify it by the number of its terms. Otherwise, tell why it is not a polynomial. 2.
ANSWER
polynomial Degree: 3, trinomial

6. EXAMPLE 3
GUIDED PRACTICE
Add polynomials
for Examples 1,2, and 3
for Example
Find the sum. 3.
(5x3 + 4x – 2x) + (4x2 +3x3 – 6)
= 8x3 + 4x2 + 2x – 6
ANSWER

7. EXAMPLE 4
Subtract polynomials
Find the difference.
a. (4n2 + 5) – (–2n2 + 2n – 4)
b. (4x2 – 3x + 5) – (3x2 – x – 8)

8. EXAMPLE 4
Subtract polynomials
SOLUTION
a (4n ) 4n
–(–2n2 + 2n – 4)
2n2 – 2n + 4
6n2 – 2n + 9
b. (4x2 – 3x + 5) – (3x2 – x – 8) =
4x2 – 3x + 5 – 3x2 + x + 8
= (4x2 – 3x2) + (–3x + x) + (5 + 8)
= x2 – 2x + 13

9. EXAMPLE 5
Solve a multi-step problem
BASEBALL ATTENDANCE
Major League Baseball teams are divided into two leagues. During the period 1995–2001, the attendance N and A (in thousands) at National and American League baseball games, respectively, can be modeled by
N = –488t t + 24,700 and
A = –318t t + 25,600
where t is the number of years since About how many people attended Major League Baseball games in 2001?

10. EXAMPLE 5
Solve a multi-step problem
SOLUTION
STEP 1
Add the models for the attendance in each league to find a model for M, the total attendance (in thousands).
M = (–488t t + 24,700) + (–318t t + 25,600)
= (–488t2 – 318t2) + (5430t t) + (24, ,600)
= –806t t + 50,300

11. EXAMPLE 5
Solve a multi-step problem
STEP 2
Substitute 6 for t in the model, because 2001 is 6 years
after 1995.
M = –806(6) (6) + 50, ,100
ANSWER
About 72,100,000 people attended Major League
Baseball games in 2001.

12. EXAMPLE 4
GUIDED PRACTICE
Subtract polynomials
for Examples 4 and 5
Find the difference. 4.
a. (4x2 – 7x) – (5x2 + 4x – 9)
–x2 – 11x + 9
ANSWER
BASEBALL ATTENDNCE Look back at Example 5. Find the difference in attendance at National and American League baseball games in 2001. 5.
ANSWER
about 7,320,000 people

13. Daily Homework Quiz
If the expression is a polynomial, find its degree and classify it by the number of terms. Otherwise, tell why it is not a polynomial.
1. m3 + n4m2 + m–2
No; one exponent is not a whole number.
ANSWER
2. – 3b3c4 – 4b2c + c8
ANSWER
8th degree trinomial

14. Daily Homework Quiz
Find the sum or difference.
3. (3m2 – 2m + 9) + (m2 + 2m – 4)
4m2 + 5
ANSWER
4. (– 4a2 + 3a – 1) – (a2 + 2a – 6)
ANSWER
–5a2 + a + 5

15. Daily Homework Quiz
5. The number of dog adoptions D and cat adoptions C can be modeled by D = 1.35 t2 – 9.8t and
C= 0.1t2 – 3t + 79 where t represents the years since About how many dogs and cats were adopted in 2004?
about 185 dogs and cats
ANSWER