NAME
DATE
8-1
PERIOD
Practice
Adding and Subtracting Polynomials
Find each sum or difference.
1. (4y + 5) + (-7y - 1)
2. (-x2 + 3x) - (5x + 2x2)
-3x2 - 2x
-3y + 4
3. (4k2 + 8k + 2) - (2k + 3)
4. (2m2 + 6m) + (m2 - 5m + 7)
4k2 + 6k - 1
5. (5a2 + 6a + 2) - (7a2 - 7a + 5)
3m2 + m + 7
6. (-4p2 - p + 9) + ( p2 + 3p - 1)
-2a2 + 13a - 3
7. (x3 - 3x + 1) - (x3 + 7 - 12x)
-3p2 + 2p + 8
8. (6x2 - x + 1) - (-4 + 2x2 + 8x)
4x2 - 9x + 5
9x - 6
9. (4y2 + 2y - 8) - (7y2 + 4 - y)
10. (w2 - 4w - 1) + (-5 + 5w2 - 3w)
-3y2 + 3y - 12
6w2 - 7w - 6
Determine whether each expression is a polynomial. If it is a polynomial, find the
degree and determine whether it is a monomial, binomial, or trinomial.
11. 7a2b + 3b2 - a2b
1 3
12. −
y + y2 - 9
5
yes; 3; binomial
yes; 3; trinomial
14. −
3
yes; 6; monomial
not a polynomial
Write each polynomial in standard form. Identify the leading coefficient.
15. 8x2 - 15 + 5x5
5
16. 10x - 7 + x4 + 4x3
2
x4 + 4x3 + 10x -7; 1
5x + 8x -15; 5
17. 13x2 - 5 + 6x3 - x
18. 4x + 2x5 - 6x3 + 2
6x3 + 13x2 - x - 5; 6
2x5 - 6x3 + 4x + 2; 2
19. BUSINESS The polynomial s3 - 70s2 + 1500s - 10,800 models the profit a company
makes on selling an item at a price s. A second item sold at the same price brings in a
profit of s3 - 30s2 + 450s - 5000. Write a polynomial that expresses the total profit from
the sale of both items. 2s3 - 100s2 + 1950s - 15,800
20. GEOMETRY The measures of two sides of a triangle are given.
If P is the perimeter, and P = 10x + 5y, find the measure of
the third side. 2x + 2y
Chapter 8
8
3x + 4y
5x - y
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
x + 3x4 - 21x2
x
13. 6g2h3k
NAME
DATE
8-2
PERIOD
Practice
Multiplying a Polynomial by a Monomial
Find each product.
1. 2h(-7h2 - 4h)
2. 6pq(3p2 + 4q)
-14h3 - 8h2
18p3q + 24pq2
3. 5jk(3jk + 2k)
4. -3rt(-2t2 + 3r)
15j2k2 + 10jk2
6rt3 - 9r2t
1
5. - −
m(8m 2 + m - 7)
2 2
6. - −
n (-9n 2 + 3n + 6)
4
3
1 2
7
-2m - −
m +−
m
4
4
3
6n4 - 2n3 - 4n2
Simplify each expression.
8. 5w(-7w + 3) + 2w(-2w2 + 19w + 2)
7. -2ℓ(3ℓ - 4) + 7ℓ
-6ℓ2 + 15ℓ
-4w3 + 3w2 + 19w
9. 6t(2t - 3) - 5(2t2 + 9t - 3)
10. -2(3m3 + 5m + 6) + 3m(2m2 + 3m + 1)
9m2 - 7m - 12
2t - 63t + 15
Lesson 8-2
2
11. -3g(7g - 2) + 3( g2 + 2g + 1) - 3g(-5g + 3) -3g2 + 3g + 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation.
12. 5(2t - 1) + 3 = 3(3t + 2) 8
13. 3(3u + 2) + 5 = 2(2u - 2) -3
1
2
14. 4(8n + 3) - 5 = 2(6n + 8) + 1 −
3
2
16. t(t + 4) - 1 = t(t + 2) + 2 −
1
4
15. 8(3b + 1) = 4(b + 3) - 9 - −
17. u(u - 5) + 8u = u(u + 2) - 4 -4
18. NUMBER THEORY Let x be an integer. What is the product of twice the integer added
to three times the next consecutive integer? 5x + 3
19. INVESTMENTS Kent invested $5000 in a retirement plan. He allocated x dollars of the
money to a bond account that earns 4% interest per year and the rest to a traditional
account that earns 5% interest per year.
a. Write an expression that represents the amount of money invested in the traditional
account. 5000 - x
b. Write a polynomial model in simplest form for the total amount of money T Kent has
invested after one year. (Hint: Each account has A + IA dollars, where A is the
original amount in the account and I is its interest rate.) T = 5250 - 0.01x
c. If Kent put $500 in the bond account, how much money does he have in his
retirement plan after one year? $5245
Chapter 8
15
Glencoe Algebra 1
NAME
DATE
8-3
PERIOD
Practice
Multiplying Polynomials
Find each product.
1. (q + 6)(q + 5)
2. (x + 7)(x + 4)
2
x2 + 11x + 28
q + 11q + 30
3. (n - 4)(n - 6)
4. (a + 5)(a - 6)
2
a2 - a - 30
n - 10n + 24
5. (4b + 6)(b - 4)
6. (2x - 9)(2x + 4)
2
4x2 - 10x - 36
4b - 10b - 24
7. (6a - 3)(7a - 4)
8. (2x - 2)(5x - 4)
2
10x2 - 18x + 8
42a - 45a + 12
9. (3a - b)(2a - b)
10. (4g + 3h)(2g + 3h)
6a2 - 5ab + b2
8g2 + 18gh + 9h2
12. (t + 3)(t2 + 4t + 7)
m3 + 9m2 + 12m - 40
13. (2h + 3)(2h2 + 3h + 4)
t3 + 7t2 + 19t + 21
14. (3d + 3)(2d2 + 5d - 2)
4h3 + 12h2 + 17h + 12
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
15. (3q + 2)(9q2 - 12q + 4)
6d3 + 21d2 + 9d - 6
16. (3r + 2)(9r2 + 6r + 4)
27q3 - 18q2 - 12q + 8
17. (3n2 + 2n - 1)(2n2 + n + 9)
27r3 + 36r2 + 24r + 8
18. (2t2 + t + 3)(4t2 + 2t - 2)
6n4 + 7n3 + 27n2 + 17n - 9
19. (2x2 - 2x - 3)(2x2 - 4x + 3)
4
3
8t4 + 8t3 + 10t2 + 4t - 6
20. (3y2 + 2y + 2)(3y2 - 4y - 5)
2
9y4 - 6y3 - 17y2 - 18y - 10
4x - 12x + 8x + 6x - 9
GEOMETRY Write an expression to represent the area of each figure.
21.
4x2 - 2x - 2 units2
22.
2x - 2
5x - 4
4x2 + 3x - 1 units2
x+1
4x + 2
3x + 2
23. NUMBER THEORY Let x be an even integer. What is the product of the next two
consecutive even integers? x2 + 6x + 8
24. GEOMETRY The volume of a rectangular pyramid is one third the product of the area of
its base and its height. Find an expression for the volume of a rectangular pyramid
whose base has an area of 3x2 + 12x + 9 square feet and whose height is x + 3 feet.
x3 + 7x2 + 15x + 9 ft3
Chapter 8
21
Glencoe Algebra 1
Lesson 8-3
11. (m + 5)(m2 + 4m - 8)
NAME
DATE
8-4
PERIOD
Practice
Special Products
Find each product.
1. (n + 9)2
2. (q + 8)2
2
n + 18n + 81
5. ( p + 7)2
2
b2 - 36
8. (4j + 2)2
7. (z + 13)(z - 13)
2
9. (5w - 4)2
2
z - 169
25w2 - 40w + 16
16j + 16j + 4
10. (6h - 1)2
11. (3m + 4)2
2
12. (7v - 2)2
2
36h - 12h + 1
49v2 - 28v + 4
9m + 24m + 16
13. (7k + 3)(7k - 3)
14. (4d - 7)(4d + 7)
49k2 - 9
15. (3g + 9h)(3g - 9h)
16d2 - 49
9g2 - 81h2
17. (a + 6u)2
16. (4q + 5t)(4q - 5t)
2
18. (5r + p)2
2
2
25r2 + 10rp + p2
a + 12au + 36u
16q - 25t
19. (6h - m)2
20. (k - 6y)2
2
2
21. (u - 7p)2
2
36h - 12hm + m
2
u2 - 14up + 49p2
k - 12ky + 36y
22. (4b - 7v)2
23. (6n + 4p)2
2
2
16b - 56bv + 49v
2
24. (5q + 6t)2
2
36n + 48np + 16p
2
27. (9x + 2y2)2
26. (8h + 3d)(8h - 3d)
2
2
36a - 49b
2
81x2 + 36xy2 + 4y4
64h - 9d
28. (3p3 + 2m)2
29. (5a2 - 2b)2
3
2
9p + 12p m + 4m
31. (6b3 - g)2
4
30. (4m3 - 2t)2
2
2
36b - 12b g + g
2
25a - 20a b + 4b
32. (2b2 - g)(2b2 + g)
3
4
2
25q2 + 60qt + 36t2
16m6 - 16m3t + 4t2
33. (2v2 + 3x2)(2v2 + 3x2)
4v4 + 12v2x2 + 9x4
4b - g
34. GEOMETRY Janelle wants to enlarge a square graph that she has made so that a side
of the new graph will be 1 inch more than twice the original side g. What trinomial
represents the area of the enlarged graph? 4g2 + 4g + 1
35. GENETICS In a guinea pig, pure black hair coloring B is dominant over pure white
coloring b. Suppose two hybrid Bb guinea pigs, with black hair coloring, are bred.
a. Find an expression for the genetic make-up of the guinea pig offspring.
0.25BB + 0.50Bb + 0.25bb
b. What is the probability that two hybrid guinea pigs with black hair coloring will
produce a guinea pig with white hair coloring? 25%
Chapter 8
28
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
25. (6a - 7b)(6a + 7b)
6
6. (b + 6)(b - 6)
p2 + 14p + 49
r - 22r + 121
6
x2 - 20x + 100
q + 16q + 64
4. (r - 11)2
2
3. (x - 10)2
2