Chapter 8
Find each sum or difference.
1. SOLUTION: ANSWER: 2. SOLUTION: ANSWER: Simplify each expression.
3. SOLUTION: ANSWER: 4. SOLUTION: eSolutions Manual - Powered by Cognero
Page 1
ANSWER: Chapter 8
4. SOLUTION: ANSWER: Solve each equation.
5. SOLUTION: ANSWER: 6. SOLUTION: ANSWER: Find each product.
7. SOLUTION: eSolutions Manual - Powered by Cognero
ANSWER: Page 2
Chapter
8
ANSWER: Find each product.
7. SOLUTION: ANSWER: 8. SOLUTION: ANSWER: 9. SIDEWALKS Reynoldsville is repairing sidewalks. If the sidewalk is the same width around a city block, write an
expression for the area of the block and the sidewalk.
SOLUTION: The sidewalk is the little border around the block. The sidewalk is the same depth throughout, so let the depth be x.
The length of the block including the sidewalk is 100 + 2x and the width is 80 + 2x.
ANSWER: Find each product.
10. SOLUTION: eSolutions Manual - Powered by Cognero
Page 3
ANSWER: Chapter 8
Find each product.
10. SOLUTION: ANSWER: 11. SOLUTION: ANSWER: 12. SOLUTION: ANSWER: 13. SOLUTION: ANSWER: Use the Distributive Property to factor each polynomial.
14. SOLUTION: Find the GCF of the terms.
eSolutions
Manual - Powered by Cognero
The GCF of 4, 16, and 8 is 4.
Page 4
2 2
Each term has at least 2 ms and 2ns, so m n is the GCF of the variable terms.
ANSWER: Chapter 8
Use the Distributive Property to factor each polynomial.
14. SOLUTION: Find the GCF of the terms.
The GCF of 4, 16, and 8 is 4.
2 2
Each term has at least 2 ms and 2ns, so m n is the GCF of the variable terms.
ANSWER: 15. SOLUTION: Find the GCF of the terms.
The GCF of 12, 36, and 3 is 3.
2k 2
Each term has at least 2 j s and 2kns, so j n is the GCF of the variable terms.
ANSWER: Factor each polynomial.
16. SOLUTION: ANSWER: 17. SOLUTION: ANSWER: eSolutions Manual - Powered by Cognero
18. HEIGHT The height h of a ball bounced off the ground after t seconds is modeled by the equation
Page 5
ANSWER: Chapter 8
17. SOLUTION: ANSWER: 18. HEIGHT The height h of a ball bounced off the ground after t seconds is modeled by the equation
a. What is the height of the ball at 1.5 seconds?
b. How many seconds before the ball hits the ground again?
SOLUTION: a. So, the height of the ball at 1.5 seconds is 7.2 feet.
b. The ball will hit the ground again when h = 0.
Thus, the ball will hit the ground again after 1.8 seconds.
ANSWER: a. 7.2 ft
b. 1.8 seconds
Factor each polynomial.
19. SOLUTION: eSolutions Manual - Powered by Cognero
ANSWER: Page 6
ANSWER: a. 7.2 ft
Chapter
8
b. 1.8 seconds
Factor each polynomial.
19. SOLUTION: ANSWER: 20. SOLUTION: ANSWER: 21. SOLUTION: ANSWER: 22. SOLUTION: ANSWER: Solve each equation. Check your solution.
23. SOLUTION: eSolutions Manual - Powered by Cognero
Page 7
ANSWER: Chapter
8
Solve each equation. Check your solution.
23. SOLUTION: Check.
ANSWER: 24. SOLUTION: ANSWER: 25. SOLUTION: eSolutions Manual - Powered by Cognero
Page 8
ANSWER: Chapter
8
25. SOLUTION: Check.
ANSWER: 26. SOLUTION: ANSWER: Factor each polynomial, if possible. If the polynomial cannot be factored using integers, write prime .
27. SOLUTION: 2(–30) = –60
FindManual
2 numbers
whose
product is –60 and whose sum is 7.
eSolutions
- Powered
by Cognero
30(–2) = –60
20(–3) = –60
Page 9
ANSWER: Chapter
8
Factor each polynomial, if possible. If the polynomial cannot be factored using integers, write prime .
27. SOLUTION: 2(–30) = –60
Find 2 numbers whose product is –60 and whose sum is 7.
30(–2) = –60
20(–3) = –60
15(–4) = –60
12(–5) = –60
Use 12 and –5.
ANSWER: 28. SOLUTION: 3(–42) = –126
Find 2 numbers whose product is –126 and whose sum is –11.
3(–42) = –39
6(–21) = 150
7(–18) = –11
Use 7 and –18.
ANSWER: 29. eSolutions
Manual - Powered by Cognero
SOLUTION: Page 10
ANSWER: Chapter
8
29. SOLUTION: 6(–5) = –30
Find 2 numbers whose product is –30 and whose sum is –13.
1(–30) = –29
2(–15) = –13
Use 2 and –15.
ANSWER: 30. SOLUTION: 11(5) = 55
There are no 2 numbers whose product is 55 and whose sum is –3. The polynomial is prime.
ANSWER: prime
31. PRIZES A machine is used to throw T-shirts into the crowd at the Hornets basketball games.
a. What is the initial height of the T-shirt?
b. If the T-shirt is caught after 2 seconds, what is the height?
SOLUTION: a. The initial height is the value of c. It is also the value when x = 0.
eSolutions Manual - Powered by Cognero
b. Set t equal to 2.
Page 11
There are no 2 numbers whose product is 55 and whose sum is –3. The polynomial is prime.
ANSWER: Chapter
8
prime
31. PRIZES A machine is used to throw T-shirts into the crowd at the Hornets basketball games.
a. What is the initial height of the T-shirt?
b. If the T-shirt is caught after 2 seconds, what is the height?
SOLUTION: a. The initial height is the value of c. It is also the value when x = 0.
b. Set t equal to 2.
ANSWER: a. 4 ft
b. 8 ft
Factor each polynomial.
32. SOLUTION: ANSWER: 33. SOLUTION: ANSWER: 34. eSolutions
Manual - Powered by Cognero
SOLUTION: Page 12
ANSWER: Chapter
8
34. SOLUTION: ANSWER: 35. SOLUTION: ANSWER: 36. SOLUTION: ANSWER: 37. SOLUTION: ANSWER: 38. FRUIT An apple fell 25 feet from a tree. The formula
seconds it will take the apple to hit the ground. a. How
long
will it take
the apple to hit the ground?
eSolutions
Manual
- Powered
by Cognero
b. If you catch it at 4 feet, for how long did the apple drop?
can be used to approximate the number of
Page 13
ANSWER: Chapter
8
38. FRUIT An apple fell 25 feet from a tree. The formula
seconds it will take the apple to hit the ground. a. How long will it take the apple to hit the ground?
b. If you catch it at 4 feet, for how long did the apple drop?
can be used to approximate the number of
SOLUTION: a.
Time is positive, so t = 5.
b. ANSWER: a. 1.25 seconds
b. about 1.15 seconds
Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.
39. SOLUTION: ANSWER: yes;
40. SOLUTION: 2
2
4 = 2Manual
and -16
= 4 , but 12 ≠ 2(2)(4)
eSolutions
Powered
by Cognero
ANSWER: no
Page 14
ANSWER: Chapter
yes; 8
40. SOLUTION: 2
2
4 = 2 and 16 = 4 , but 12 ≠ 2(2)(4)
ANSWER: no
41. SOLUTION: ANSWER: yes;
42. SOLUTION: ANSWER: yes;
eSolutions Manual - Powered by Cognero
Page 15