1. Add and Subtract Polynomials
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm-Up
Simplify the expression.
1. 5x + 4(2x + 7)
ANSWER
13x + 28
2. 9x – 6(x + 2) + 3
ANSWER
3x – 9
3. Imported square tiles used for a kitchen floor measure 18 centimeters on one side. What is the area of a floor
composed of 50 tiles? Use A = s2 for the area of a tile.
ANSWER
16,200 cm2

3. Example 1
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.

4. Guided Practice
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

5. Example 2
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.
7bc3 + 4b4c
n– 2 – 3
6n4 – 8n
2x2 + x – 5 9
Classify by degree and number of terms
Is it a polynomial?
Expression a. b. c. d. e.
Yes
0 degree monomial
Yes
2nd degree trinomial
No; variable exponent
No; variable exponent
Yes
5th degree binomial

6. Guided Practice
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

7. Example 2
Find the sum.
a. (2x3 – 5x2 + x) + (2x2 + x3 – 1)
b. (3x2 + x – 6) + (x2 + 4x + 10)
SOLUTION
a. Vertical format: Align like terms in vertical columns.
(2x3 – 5x2 + x)
+ x3 + 2x – 1
3x3 – 3x2 + x – 1

8. Example 2
b. Horizontal format: Use the associative and commutative properties to group like terms. Then simplify.
(3x2 + x – 6) + (x2 + 4x + 10) =
(3x2 + x2) + (x + 4x) + (– )
= 4x2 + 5x + 4

9. Guided Practice
Find the sum 3.
(5x3 + 4x – 2x) + (4x2 +3x3 – 6)
= 8x3 + 4x2 + 2x – 6
ANSWER

10. Example 4
Find the difference.
a. (4n2 + 5) – (–2n2 + 2n – 4)
b. (4x2 – 3x + 5) – (3x2 – x – 8)
SOLUTION
a (4n ) 4n
–(–2n2 + 2n – 4)
2n2 – 2n + 4
6n2 – 2n + 9

11. Example 4
b. (4x2 – 3x + 5) – (3x2 – x – 8) =
4x2 – 3x + 5 – 3x2 + x + 8
= (4x2 – 3x2) + (–3x + x) + (5 + 8)
= x2 – 2x + 13

12. Guided Practice
Find the difference 4.
(4x2 – 7x) – (5x2 + 4x – 9)
–x2 – 11x + 9
ANSWER

13. Example 5
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?

14. Example 5
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

15. Example 5
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.

16. Guided Practice
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

17. Lesson 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

18. Lesson 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
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