9-1
Adding and Subtracting
Polynomials
9-1
1. Plan
Objectives
1
2
To describe polynomials
To add and subtract
polynomials
Examples
1
2
3
4
Degree of a Monomial
Classifying Polynomials
Adding Polynomials
Subtracting Polynomials
Math Background
What You’ll Learn
Check Skills You’ll Need
• To describe polynomials
• To add and subtract
Simplify each expression.
polynomials
To combine and simplify
polynomials, as in Example 4
6. 8x 2 - x 2 7x2
Activity: Using Polynomials
Business Suppose you work at a pet store. The spreadsheet below shows
the details of several customers’ orders.
2. Davis: 24m
1
2
3
4
5
Martino:
3.99s ± 2.29g ± 1.89p
B
A
C
D
E
F
Customer Seed Cuttlebone Millet G. Paper Perches
Davis
✔
Brooks
✔
✔
Casic
✔
✔
Martino ✔
✔
✔
The following variables represent the number of each item ordered.
s = bags of birdseed
c = packages of cuttlebone
p = packages of perches
Bell Ringer Practice
Check Skills You’ll Need
Rocky's Friends
Bird Supplies
For intervention, direct students to:
bird seed (5 lb)
cuttlebone (2 ct)
spray millet (5 lb)
gravel paper (1 pkg)
perches (2 ct)
$3.99
$2.00
$24.00
$2.29
$1.89
494
m = bags of millet
g = packages of gravel paper
1. Which expression represents the cost of Casic’s order? B
A. 27.99(s + m)
B. 3.99s + 24m
C. 27.99sm
2. Write expressions to represent each of the other customers’ orders.
See left.
3. Martino buys 10 bags of birdseed, 4 packages of gravel paper, and
2 packages of perches. What is the total cost of his order? $52.84
A monomial is an expression that is a number, a variable, or a product of a
number and one or more variables. Each of the following is a monomial.
12
y
-5x 2 y
Below Level
L2
c
3
Chapter 9 Polynomials and Factoring
Special Needs
L1
Display the activity. Have students write the
expression for Brooks’ order. 3.99s 2c. Ask for
student volunteers to point out how they picked up
the data and built the expression.
494
3. 7k - 15k –8k
1
PowerPoint
Lesson 2-4: Example 5
Extra Skills and Word
Problem Practice, Ch. 2
-
7n 2 –3n2
Part
1 1 Describing Polynomials
See p. 492E for a list of the
resources that support this lesson.
The Distributive Property
5.
4n 2
Lesson 2-4
New Vocabulary • monomial • degree of a monomial • polynomial
• standard form of a polynomial • degree of a polynomial
• binomial • trinomial
Brooks: 3.99s ± 2c
Lesson Planning and
Resources
2. 5g + 34g 39g
4. 2b - 6 + 9b 11b – 6
. . . And Why
A polynomial is made up of terms,
which are algebraic expressions
combined by addition or
subtraction. In a polynomial,
there are no expressions that
involve dividing by the variable or
taking any root of a variable.
More Math Background: p. 492C
1. 6t + 13t 19t
GO for Help
learning style: visual
Show students that 3c is a monomial because it can be
rewritten as c ? 13 . However, since xc = c ? 1x , it does
not fit the definition of a monomial.
learning style: verbal
Vocabulary Tip
The prefix mono means
“one.”
1
The fraction 3c is a monomial, but the expression xc is not a monomial because there
is a variable in the denominator.
2. Teach
The degree of a monomial is the sum of the exponents of its variables. For a
nonzero constant, the degree is 0. Zero has no degree.
Guided Instruction
Activity
Degree of a Monomial
EXAMPLE
Diversity
Find the degree of each monomial.
a. 23 x
Quick Check
b. 7x2y3
Degree: 5
2 x = 2 x 1. The exponent is 1.
3
3
The exponents are 2 and 3. Their sum is 5.
c. -4
Degree: 0
The degree of a nonzero constant is 0.
Degree: 1
Ask knowledgeable students to
describe the purpose of the bird
supplies.
1
9x0?
1 Critical Thinking What is the degree of
Explain.
0; the degree of a nonzero constant is 0.
A polynomial is a monomial or the sum or difference of two or more monomials.
degree S
3x 4 + 5x 2 - 7x + 1
c
c
c
c
4
2
1
0
After you simplify a polynomial by combining like terms, you can name the
polynomial based on its degree or the number of monomials it contains.
Name Using
Number of Terms
7x 4
1
linear
2
binomial
2x 1
2
quadratic
3
trinomial
4x3
3
cubic
1
monomial
9x 11x
4
fourth degree
2
binomial
5
0
constant
1
monomial
EXAMPLE
b. 3x 4 - 4 + 2x 2 + 5x4
Place terms in order.
linear binomial
c. –4v ± 8;
linear binomial
3x 4 + 5x 4 + 2x 2 - 4
Place terms in order.
8x 4 + 2x 2 - 4
Combine like terms.
fourth degree trinomial
Quick Check
2 Write each polynomial in standard form. Then name each polynomial based on its
degree and the number of its terms. See left.
a. 6x 2 + 7 - 9x 4
b. 3y - 4 - y 3
c. 8 + 7v - 11v
Lesson 9-1 Adding and Subtracting Polynomials
Advanced Learners
5 2
14 x
1
2
3x
2 5 -
17 x2
1
1
2x
2 Write each polynomial in
standard form. Then name each
polynomial based on its degree
and the number of its terms.
a. -2 + 7x 7x – 2; linear
binomial
b. 3x5 - 2 - 2x5 + 7x
x 5 ± 7x – 2; fifth degree
trinomial
495
English Language Learners ELL
L4
Have students simplify
21 x2
Have each student write a
polynomial similar to one shown
in the table above Example 2.
Redistribute the papers. Direct
students to move, using
instructions such as: All linear
binomials go to the front of the
room. All cubic monomials go to
the windows. Use different
combinations of polynomial
names until all students have
moved to an area of the room.
Have students check with each
other to make sure they are in the
correct locations.
1 Find the degree of each
monomial.
a. 18 0
b. 3xy 3 4
c. 6c 1
Classifying Polynomials
a. 5 - 2x
-2x + 5
Tactile Learners
Additional Examples
Write each polynomial in standard form. Then name each polynomial based on its
degree and the number of its terms.
b. –y3 ± 3y – 4;
cubic trinomial
EXAMPLE
PowerPoint
4
2a. –9x4 ± 6x2 ± 7;
fourth degree
trinomial
Number
of Terms
Degree
3x2
2
Name Using
Degree
Polynomial
Math Tip
Explain to students that it is
reasonable that the degree of -4
is 0 because -4 can be written as
-4x 0, for x 2 0.
2
The polynomial shown above is in standard form. Standard form of a polynomial
means that the degrees of its monomial terms decrease from left to right. The
degree of a polynomial in one variable is the same as the degree of the
monomial with the greatest exponent. The degree of 3x 4 + 5x 2 - 7x + 1 is 4.
EXAMPLE
2
1
5 .
1 16x 2 21
5
learning style: verbal
Ask: What numbers do the first syllables of each of
the terms monomial, binomial, and trinomial make
you think of? 1, 2, 3 What does poly mean on the
front of a word? many Stress that this number refers
to the number of terms in an expression.
learning style: verbal
495
3
EXAMPLE
Alternative Method
Use tiles to demonstrate adding
polynomials. Have students model
each polynomial. Group like tiles
together. Remove zero pairs. Then
write an expression for the
remaining tiles. Remind students
that red tiles represent negative
amounts.
4
EXAMPLE
2
1 2 Adding and Subtracting Polynomials
Part
You can add polynomials by adding like terms.
3
Adding Polynomials
Simplify A 4x 2 + 6x + 7 B + A 2x 2 - 9x + 1 B .
Method 1 Add vertically.
Error Prevention
Remind students to distribute the
negative sign to all terms in the
second parentheses. You may
want to encourage students to
mark the terms, such as by circling
the whole parentheses, as a
reminder.
EXAMPLE
Line up like terms. Then add the coefficients.
4x 2 + 6x + 7
1 2x 2 2 9x 1 1
6x2 - 3x + 8
For: Polynomial Addition Activity
Use: Interactive Textbook, 9-1
Method 2 Add horizontally.
Group like terms. Then add the coefficients.
A 4x 2 + 6x + 7 B + A 2x 2 - 9x + 1 B = A 4x 2 + 2x 2 B + (6x - 9x) + (7 + 1)
PowerPoint
= 6x2 - 3x + 8
Additional Examples
Quick Check
3 Simplify
3 Simplify each sum. 20m 2 ± 9
a. A12m 2 + 4 B + A8m2 + 5 B
b. A t2 - 6 B + A 3t2 + 11 B 4t2 ± 5
d. A 2p3 + 6p2 + 10p B + A 9p3 + 11p2 + 3p B
11p3 ± 17p2 ± 13p
(6x2 + 3x + 7) + (2x2 - 6x - 4).
8x2 – 3x ± 3
c. A 9w 3 + 8w 2 B + A 7w3 + 4 B
16w3 ± 8w2 ± 4
4 Simplify
(2x3 + 4x2 - 6) - (5x3 + 2x - 2).
–3x3 ± 4x2 – 2x – 4
In Chapter 1, you learned that subtraction means to add the opposite. So when
you subtract a polynomial, change each of the terms to its opposite. Then add
the coefficients.
4
Resources
• Daily Notetaking Guide 9-1 L3
• Daily Notetaking Guide 9-1—
L1
Adapted Instruction
EXAMPLE
Subtracting Polynomials
Simplify A 2x3 + 5x2 - 3x B - A x3 - 8x2 + 11 B .
Method 1 Subtract vertically.
2x 3 + 5x 2 - 3x
2 Ax 3 2 8x 2 1 11B
Closure
2x 3 + 5x2 - 3x
2x 3 1 8x 2 2 11
Say the name of a polynomial
using its degree and number of
terms. Instruct students to write a
polynomial to match the name.
Repeat for different types of
polynomials. Let students choose
two of the polynomials to both
add and subtract.
Line up like terms.
Then add the opposite of each term in the polynomial
being subtracted.
x 3 + 13x2 - 3x1- 11
Method 2 Subtract horizontally.
A 2x 3 + 5x 2 - 3x B - A x 3 - 8x 2 + 11 B
4a. –8v3 ± 13v2 – 4v
b. 28d 3 – 30d 2 – 3d
Quick Check
= 2x 3 + 5x2 - 3x - x 3 + 8x 2 - 11
Write the opposite of each term in the
polynomial being subtracted.
= A 2x 3 - x 3 B + A 5x 2 + 8x 2 B - 3x - 11
Group like terms.
= x 3 + 13x 2 - 3x - 11
Simplify.
4 Simplify each difference. a–b. See left.
a. Av 3 + 6v 2 - v B - A 9v 3 - 7v 2 + 3v B
b. A 30d 3 - 29d 2 - 3d B - A 2d 3 + d 2 B
c. A 4x 2 + 5x + 1 B - A 6x 2 + x + 8 B –2x2 ± 4x – 7
496
Chapter 9 Polynomials and Factoring
pages 497–499
Exercises
15. –3x2 ± 4x;
quadratic binomial
16. 4x ± 9;
linear binomial
496
17. c2 ± 4c – 2;
quadratic trinomial
18. –2z2 ± 5z – 5;
quadratic trinomial
19. 15y8 – 7y 3 ± y;
eighth degree trinomial
EXERCISES
For more exercises, see Extra Skill and Word Problem Practice.
3. Practice
Practiceand
andProblem
ProblemSolving
Solving
Practice
Assignment Guide
A
Practice by Example
Example 1
(page 495)
GO for
Help
Find the degree of each monomial.
1. 4x 1
2. 7c 3 3
3. -16 0
4. 6y 2w 8 10
5. 8ab3 4
6. 6 0
7. -9x4 4
8. 11 0
1 A B 1-20, 42, 51
2 A B
C Challenge
Example 2
(page 495)
9. quadratic trinomial
10. linear binomial
11. cubic trinomial
Name each expression based on its degree and number of terms. 9–11. See left.
10. 3 z + 5
9. 5x2 - 2x + 3
11. 7a3 + 4a - 12
4
12. x3 + 5
13. -15
14. w2 + 2
constant monomial
not a polynomial
quadratic binomial
Write each polynomial in standard form. Then name each polynomial based on its
degree and number of terms. 15–20. See margin p. 496.
15. 4x - 3x 2
16. 4x + 9
17. c 2 - 2 + 4c
18. 9z2 - 11z2 + 5z - 5
19. y - 7y 3 + 15y 8
20. -10 + 4q 4 - 8q + 3q 2
21-41, 43-50
52-55
Test Prep
Mixed Review
56-62
63-86
Homework Quick Check
To check students’ understanding
of key skills and concepts, go over
Exercises 12, 24, 36, 39, 42.
Error Prevention!
Exercises 15–20 Many students
Example 3
(page 496)
Simplify each sum. 25–27. See margin.
24. A 8x 2 + 1 B + A 12x 2 + 6 B 20x2 ± 7
+ w-4
2 4w 1 8
8w2 – 3w ± 4
25. A g 4 + 4g B + A 9g 4 + 7g B
26. A a 2 + a + 1 B + A 5a 2 - 8a + 20 B
27. A 7y 3 - 3y 2 + 4y B + A 8y 4 + 3y 2 B
21.
1
5m2
3m2
+9
16
8m2
± 15 22.
3k - 8 10k ± 4
1 7k 1 12
23.
1
w2
7w2
forget that the sign in front of a
term must move with the term.
Have students circle each term,
including the sign in front of the
term. Everything that is inside
each circle must move together.
Error Prevention!
(page 496)
Simplify each difference. 28–32. See margin.
28.
6c - 5
2 (4c 1 9)
29.
2b + 6
2(b 1 5)
31. A 17n 4 + 2n 3 B - A 10n 4 + n 3 B
B
35.
18y2
Apply Your Skills
± 5y
36. –6x3 ± 3x2 – 4
37. –7z 3 ± 6z2 ± 2z – 5
38. 7a3 ± 11a2 – 4a – 4
30.
Exercise 23 Some students may
7h2 + 4h - 8
2 A3h2 2 2h 1 10B
use zero for the coefficient of w.
Remind them that w means 1w.
32. A 24x 5 + 12x B - A 9x 5 + 11x B
Exercises 49, 50 Tell students
33. A 6w 2 - 3w + 1 B - A w 2 + w - 9 B
34. A -5x 4 + x 2 B - A x 3 + 8x 2 - x B
2
–5x4 – x3 – 7x2 ± x
5w – 4w ± 10
Simplify. Write each answer in standard form. 35–38. See left.
35. A 7y 2 - 3y + 4y B + A 8y2 + 3y 2 + 4y B 36. A 2x 3 - 5x 2 - 1 B - A 8x 3 + 3 - 8x 2 B
37. A -7z 3 + 3z - 1 B - A -6z2 + z + 4 B
these are multi-step problems in
which they must add the known
sides before subtracting from the
perimeter.
38. A 7a 3 - a + 3a 2 B + A 8a 2 - 3a - 4 B
Geometry Find an expression for the perimeter of each figure.
GPS 39. 28c – 16
40. 39x – 7
9c 10
9x
GPS Guided Problem Solving
8x 2
5x 1
5c 2
L4
Enrichment
L2
Reteaching
17x 6
Practice
Name
(5x 2
3x 1) (2 x 2 4x 2)
5x 2
5x 2
3x 2
2x 2 3x 1 4x 2
2 x 2 3 x 4x 1 2
7x 1
20.
25.
26.
4q4
3q2
7y 3
±
– 8q – 10;
fourth degree polynomial
with 4 terms
28. 2c – 14
10g4
29. b ± 1
6a2
± 11g
– 7a ± 21
27.
8y4
30.
4h2
31.
7n4
±
± 4y
± 6h – 18
±
n3
32.
15x5
497
±x
41. Kwan did not take the
opposite of each term in
the polynomial being
subtracted.
Class
Practice 9-1
Date
L3
Adding and Subtracting Polynomials
Write each polynomial in standard form. Then name each polynomial based
on its degree and number of terms.
1. 4y3 - 4y2 + 3 - y
2. x2 + x4 - 6
4. 2m2 - 7m3 + 3m
5. 4 - x + 2x2
7.
n2 - 5n
3. x + 2
6. 7x3 + 2x2
8. 6 + 7x2
9. 3a2 + a3 - 4a + 3
10. 5 + 3x
11. 7 - 8a2 + 6a
12. 5x + 4 - x2
13. 2 + 4x2 - x3
14. 4x3 - 2x2
15. y2 - 7 - 3y
16. x - 6x2 - 3
17. v3 - v + 2v2
18. 8d + 3d2
Simplify. Write each answer in standard form.
19.
Lesson 9-1 Adding and Subtracting Polynomials
L1
Adapted Practice
41. Error Analysis Kwan’s work is shown below. What mistake did he make?
See margin.
L3
(3x2 - 5x) - (x2 + 4x + 3)
20.
(2x3 - 4x2 + 3) + (x3 - 3x2 + 1)
21. (3y3 - 11y + 3) - (5y3 + y2 + 2)
22. (3x2 + 2x3) - (3x2 + 7x - 1)
23. (2a3 + 3a2 + 7a) + (a3 + a2 - 2a)
24. (8y3 - y + 7) - (6y3 + 3y - 3)
25. (x2 - 6) + (5x2 + x - 3)
26. (5n2 - 7) - (2n2 + n - 3)
27. (5n3 + 2n2 + 2) - (n3 + 3n2 - 2)
28. (3y2 - 7y + 3) - (5y + 3 - 4y2)
29. (2x2 + 9x - 17) + (x2 - 6x - 3)
30. (3 - x3 - 5x2) + (x + 2x3 - 3)
31. (3x + x2 - x3) - (x3 + 2x2 + 5x)
32. (d2 + 8 - 5d) - (5d2 + d - 2d3 + 3)
33. (3x3 + 7x2) + (x2 - 2x3)
34. (6c2 + 5c - 3) - (3c2 + 8c)
35. (3y2 - 5y - 7) + (y2 - 6y + 7)
36. (3c2 - 8c + 4) - (7 + c2 - 8c)
37. (4x2 + 13x + 9) + (12x2 + x + 6)
38. (2x - 13x2 + 3) - (2x2 + 8x)
39.
(7x - 4x2 + 11) + (7x2 + 5)
40. (4x + 7x3 - 9x2) + (3 - 2x2 - 5x)
41. (y3 + y2 - 2) + (y - 6y2)
42. (x2 - 8x - 3) - (x3 + 8x2 - 8)
43. (3x2 - 2x + 9) - (x2 - x + 7)
44. (2x2 - 6x + 3) - (2x + 4x2 + 2)
45. (2x2 - 2x3 - 7) + (9x2 + 2 + x)
46. (3a2 + a3 - 1) + (2a2 + 3a + 1)
47. (2x2 + 3 - x) - (2 + 2x2 - 5x)
48. (n4 - 2n - 1) + (5n - n4 + 5)
(x3 + 3x) - (x2 + 6 - 4x)
50. (7s2 + 4s + 2) + (3s + 2 - s2)
49.
51. (6x2 - 3x + 9) - (x2 + 3x - 5)
52. (3x3 - x2 + 4) + (2x3 - 3x + 9)
53. (y3 + 3y - 1) - (y3 + 3y + 5)
54. (3 + 5x3 + 2x) - (x + 2x2 + 4x3)
55. (x2 + 15x + 13) + (3x2 - 15x + 7)
56. (7 - 8x2) + (x3 - x + 5)
57. (2x + 3) - (x - 4) + (x + 2)
58. (x2 + 4) - (x - 4) + (x2 - 2x)
© Pearson Education, Inc. All rights reserved.
Example 4
497
4. Assess & Reteach
GO
PowerPoint
nline
Homework Help
Visit: PHSchool.com
Web Code: ate-0901
Lesson Quiz
Simplify. Write each answer in standard form. 43–48. See margin.
Write each expression in standard
form. Then name each polynomial
by its degree and number of
terms.
1. -4 + 3x - 2x2
–2x2 ± 3x – 4;
quadratic trinomial
44. (6g - 7g8) - (4g + 2g3 + 11g2)
45. (2h4 - 5h9) - (-8h5 + h10)
46. (-4t4 - 9t + 6) + (13t + 5t4)
47. (8b - 6b7 + 3b8) + (2b7 - 5b9)
48. (11 + k3 - 6k4) - (k2 - k4)
49. Perimeter = 25x + 8
50. Perimeter = 23a - 7
9a – 6
5x 2
Challenge
52a. y ≠ 2x – 1;
y ≠ 0.5x ± 3
c. 83 or 2 32
d. The lines intersect
at
x ≠ 2 23.
51. Critical Thinking Is it possible to write a binomial with degree 0? Explain.
No; both terms of a binomial cannot be constants.
52. a. Write the equations for line P and line Q.
y
P
Q
Use slope-intercept form. a, c–d. See left.
6
b. Use the expressions on the right side of each
equation to write a function for the vertical
4
distance D(x) between points on lines P and
2
Q with the same x-value. D(x) ≠ 1.5x – 4
c. For what value of x does D(x) equal zero?
O
d. Critical Thinking How does the x-value in
2
2
4
6 x
1
part (c) relate to the graph?
Simplify each expression.
53. (ab2 + ba3) + (4a3b - ab2 - 5ab)
54. (9pq6 - 11p4q) - (-5pq6 + p4q4)
3
5a b – 5ab
–p4q4 – 11p4q ± 14pq6
55. Graduation You can model the number of men and women in the United
States who enrolled in college within a year of graduating from high school
with the linear equations shown below. Let t equal the year of enrollment, with
t = 0 corresponding to 1990. Let m(t) equal the number of men in thousands,
and let w(t) equal the number of women in thousands.
Exercises
42a. monogram: a design
composed of one or
more letters, typically
the initials of a name;
used as an identifying
mark
binocular: relating to,
used by, or involving
both eyes at the same
time
tricuspid: having three
cusps, usually said of a
molar tooth
polyglot: a person with a
speaking, reading, or
writing knowledge of
several languages
8a 9
5x ± 18
C
Direct one student to state the
name of a polynomial. Instruct
another student to give an
example of the named
polynomial. Write the polynomial
on the board. Let another student
name a polynomial. Ask another
student to give an example of the
polynomial while you write it
next to the previous polynomial.
On their own pieces of paper,
have each student add the two
polynomials, write the new
polynomial in standard form, and
write its name. Repeat for
subtraction.
6a 8
6x 8
4. (-3r + 4r 2 - 3) (4r 2 + 6r - 2) –9r – 1;
linear binomial
Alternative Assessment
5x 4
4x
3. (2x 4 + 3x - 4) +
(-3x + 4 + x 4) 3x 4; fourth
degree monomial
498
43. (x3 + 3x) + (12x - x4)
Geometry Find an expression for each missing length.
2. 2b2 - 4b3 + 6
–4b3 + 2b2 ± 6;
cubic trinomial
pages 497–499
42. a. Writing Write the definition of each word. Use a dictionary if necessary.
monogram
binocular
tricuspid
polyglot a–b. See margin.
b. Open-Ended Find other words that begin with mono, bi, tri, or poly.
c. Do these prefixes have meanings similar to those in mathematics? yes
Real-World
Connection
There were about 12 million
students enrolled in college in
1980, 13.8 million in 1990,
and 15 million in 2000.
498
m(t) = 35.4t + 1146.8
men enrolled in college
w(t) = 21.6t + 1185.5
women enrolled in college
a. Add the expressions on the right side of each equation to model the total
number of recent high school graduates p(t) who enrolled in college between
1990 and 1998. p(t) ≠ 57t ± 2332.3
b. Use the equation you created in part (a) to find the number of high school
graduates who enrolled in college in 1995. 2,617,300
c. Critical Thinking If you had subtracted the expressions on the right
side of each equation above, what information would the resulting
expression model? the difference between the number of men and
the number of women enrolled in a college
Chapter 9 Polynomials and Factoring
b. Answers may vary.
Sample: monopoly,
biathlon, tripod,
polychrome
43. –x4 ± x3 ± 15x
46. t4 ± 4t ± 6
44. –7g8 – 2g3 – 11g2 ± 2g
47. –5b9 ± 3b8 – 4b7 ± 8b
45. –h10 – 5h9 ± 8h5 ± 2h4
48. –5k4 ± k3 – k2 ± 11
Test Prep
Test Prep
Standardized
Test Prep
Multiple Choice
Resources
56. Which expression represents the sum of an odd integer n and the next
three odd integers? D
A. n + 6
B. n + 12
C. 4n + 6
D. 4n + 12
57. Simplify (8x 2 + 3) + (7x2 + 10). G
F. x 2 - 7
G. 15x 2 + 13
H. 15x 4 + 13
J. 56x 4 + 30
58. Which sum is equivalent to (11k2 + 3k + 1)? A
A. (4k2 + k - 5) + (7k2 + 2k + 6)
B. (k2 - 2) + (11k2 + 3k + 3)
C. (8k2 + k) + (3k + 1)
D. (5k + 1) + (6k - 3)
Exercise 56 Explain to students
that since they are finding the
sum of four terms, each
containing n, the result must
include 4n. Tell students to
always be careful when working
with integer problems. If the
problem has consecutive odd or
consecutive even integers, each
term increases by 2, not 1.
59. How many terms does the following sum have when it is written in
standard form? (4x 9 - 3x 2 + 10x - 4) + (4x9 + x 3 + 2x ) G
F. 7
G. 5
H. 3
J. 1
60. Simplify (x 3 + x 2 + 4x) - (x2 - 5x + 6). C
A. 4x + 10
B. 4x 2 - 2x
3
D. x 3 + 2x 2 - x + 6
C. x + 9x - 6
Short Response
61. [2] 2(3x – 2) +
2(x + 2) = 6x – 4 +
2x + 4 = 8x
[1] no work shown
For additional practice with a
variety of test item formats:
• Standardized Test Prep, p. 545
• Test-Taking Strategies, p. 540
• Test-Taking Strategies with
Transparencies
61. Write and simplify a polynomial
expression that represents the perimeter
of the rectangle. Show your work.
See left.
62. Simplify (9x 3 - 4x 2 + 1) - (x2 + 2).
Show your work. See margin.
x 2
3x 2
Mixed Review
GO for
Help
Lesson 8-8
Identify the growth factor in each function.
63. y = 6 ? 2x 2
64. y = 0.6 ? 1.4x 1.4 65. y = 2 ? 5x 5
66. y = 0.3 ? 5x 5
Identify each function as exponential growth or exponential decay. 67–70. See
margin.
68. y = 1.8 ? 0.4x
69. y = 0.3 ? 7x
70. y = 0.3 ? 0.5x
67. y = 10 ? 3x
Lesson 8-3
Simplify each expression. 74–78. See left.
74. 3a3b2
71. 78 ? 710 718
72. 26 ? 2-7 12
73. (4x2)(9x3) 36x5
74. (3ab)(a2b)
75. 230
7
75. (-5t2)(6t–9)
76. (-3)6 ? (-3)–4
77. (6h2)(-2h8)
78. (2q5)(5q2)
t
76. (–3)2
77. –12h10
78. 10q7
Lesson 6-8
Write an equation for each translation of y ≠ » x ». 79–82. See margin.
79. 5 units up
80. right 6 units
81. 12 units down
82. 7 units up
83. left 10 units
y 5 »x 1 10»
84. left 0.4 units
y 5 »x 1 0.4»
85. 5.2 units up
y 5 »x» 1 5.2
86. 2.3 units down
y 5 »x» 2 2.3
lesson quiz, PHSchool.com, Web Code: ata-0901
62. [2] (9x3 – 4x2 ± 1) – (x2 ± 2) ≠
9x3 – 4x2 ± 1 – x2 – 2 ≠
(9x3) ± (–4x2 – x2 ) ± (1 – 2) ≠
9x3 – 5x2 – 1
[1] one incorrect term OR no work
shown
Lesson 9-1 Adding and Subtracting Polynomials
499
67. exponential growth
79. y 5 »x» 1 5
68. exponential decay
80. y 5 »x 2 6»
69. exponential growth
81. y 5 »x» 2 12
70. exponential decay
82. y 5 »x» 1 7
499