9.1 Add and Subtract Polynomials
Warm Up
Lesson Presentation
Lesson Quiz
9.1
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
9.1
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 – x3 +15 + 3. The
greatest degree is 3, so the degree of the polynomial is
3, and the leading coefficient is –1.
9.1
1.
Guided Practice
Write 5y – 2y2 + 9 so that the exponents decrease
from left to right. Identify the degree and leading
coefficient of the polynomial.
ANSWER
– 2y2 +5y + 9 Degree: 2, Leading Coefficient: –2
9.1
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.
Expression Is it a polynomial?
Classify by degree and
number of terms
a.
9
Yes
0 degree monomial
b.
c.
d.
e.
2x2 + x – 5
Yes
2nd degree trinomial
6n4 – 8n
No; variable exponent
n– 2 – 3
No; variable exponent
7bc3 + 4b4c
Yes
5th degree binomial
9.1
2.
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.
ANSWER
polynomial Degree: 3, trinomial
9.1
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 + 2x2
–1
3x3 – 3x2 + x – 1
9.1
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) + (– 6 + 10)
= 4x2 + 5x + 4
9.1
3.
Guided Practice
Find the sum (5x3 + 4x – 2x) + (4x2 +3x3 – 6) .
ANSWER
= 8x3 + 4x2 + 2x – 6
9.1
Example 4
Find the difference.
a. (4n2 + 5) – (–2n2 + 2n – 4)
b.
(4x2 – 3x + 5) – (3x2 – x – 8)
SOLUTION
a.
(4n2
+ 5)
–(–2n2 + 2n – 4)
4n2
+5
2n2 – 2n + 4
6n2 – 2n + 9
9.1
Example 4
b. (4x2 – 3x + 5) – (3x2 – x – 8) = 4x2 – 3x + 5 – 3x2 + x + 8
= (4x2 – 3x2) + (–3x + x) + (5 + 8)
= x2 – 2x + 13
9.1
4.
Guided Practice
Find the difference (4x2 – 7x) – (5x2 + 4x – 9) .
ANSWER
–x2 – 11x + 9
9.1
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 = –488t2 + 5430t + 24,700 and
A = –318t2 + 3040t + 25,600
where t is the number of years since 1995. About
how many people attended Major League Baseball
games in 2001?
9.1
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 = (–488t2 + 5430t + 24,700) + (–318t2 + 3040t + 25,600)
= (–488t2 – 318t2) + (5430t + 3040t) + (24,700 + 25,600)
= –806t2 + 8470t + 50,300
9.1
Example 5
STEP 2
Substitute 6 for t in the model, because 2001 is 6 years
after 1995.
M = –806(6)2 + 8470(6) + 50,300
72,100
ANSWER
About 72,100,000 people attended Major League
Baseball games in 2001.
9.1
Guided Practice
5. BASEBALL ATTENDNCE Look back at Example 5.
Find the difference in attendance at National and
American League baseball games in 2001.
ANSWER
about 7,320,000 people
9.1
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
ANSWER
2.
No; one exponent is not a whole
number.
– 3b3c4 – 4b2c + c8
ANSWER
8th degree trinomial
9.1
Lesson Quiz
Find the sum or difference.
3.
(3m2 – 2m + 9) + (m2 + 2m – 4)
ANSWER
4m2 + 5
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 + 131 and
C= 0.1t2 – 3t + 79 where t represents the years since
1998. About how many dogs and cats were adopted
in 2004?
ANSWER
about 185 dogs and cats