NAME
8-5
DATE PERIOD
Factor each polynomial.
1. 64 40 ab
8(8 5 ab )
4. 15 ad + 30 a 2 d 2
15 ad (1 + 2 ad )
7. 30 x 3
5 x 2 y + 35 x 2 y 2 y (6 x + 7 y )
10. 8 p 2 r 2 24 pr 3
8 pr ( pr 3 r
+ 16 pr
2 + 2)
13. x 2 + 4 x + 2 x + 8
( x + 2)( x + 4)
16. 6 xy 8 x + 15 y 20
(2 x + 5)(3 y 4)
2. 4 d 2 + 16
4( d 2 + 4)
5. 32 a 2 + 24 b 2
8(4 a 2 + 3 b 2 )
8. 9 a 3 d 2 6 ad 3
3 ad 2 (3 a 2 2 d )
3. 6 r 2 t 3 rt 2
3 rt (2 r t )
6. 36 xy 2 48 x 2 y
12 xy (3 y 4 x )
9. 75 b 2 g 3 + 60 bg 3
15 bg 3 (5 b + 4)
11. 5 x 3 y 2 + 10 x 2 y + 25 x
5 x ( x 2 y 2 + 2 xy + 5)
14. 2 a 2 + 3 a + 6 a + 9
( a + 3)(2 a + 3)
12. 9 ax 3 + 18 bx
3 x (3 ax 2
2 + 24 cx
+ 6 bx + 8 c )
15. 4 b 2 12 b + 2 b 6
(4 b + 2)( b 3)
17. 6 mp + 4 m + 18 p 12 18. 12 a 2 15 ab 16 a + 20 b
( 2 m + 6)(3 p 2) (3 a 4)(4 a 5 b )
Solve each equation. Check your solutions.
19. x ( x 32) = 0
{ 0, 32 }
22. ( a + 6)(3 a 7) = 0
6,
7
3
#
25. 2 z 2 + 20 z = 0
{10, 0 }
28. 18 x 2 = 15 x
0,
5
6
#
20. 4 b ( b + 4) = 0
{4, 0 }
23. (2 y + 5)( y 4) = 0
-
5
2
, 4
#
26. 8 p 2 4 p = 0
0,
1 #
29. 14 x 2 = 21 x
-
3
2
, 0
#
21. ( y 3)( y + 2) = 0
{2, 3 }
24. (4 y + 8)(3 y 4) = 0
2,
4
3
#
27. 9 x 2 = 27 x
{ 0, 3 }
30. 8 x 2 = 26 x
-
13
4
, 0
#
31.
A landscaping company has been commissioned to design a triangular flower bed for a mall entrance. The final dimensions of the flower bed have not been determined, but the company knows that the height will be two feet less than the base.
The area of the flower bed can be represented by the equation A = −
2 b 2 b .
a. Write this equation in factored form. A = b
(
1 b 1
) b. Suppose the base of the flower bed is 16 feet. What will be its area? 112 ft 2
32.
Mr. Alim’s science class launched a toy rocket from ground level with an initial upward velocity of 60 feet per second. The height h of the rocket in feet above the ground after t seconds is modeled by the equation h = 60 t 16 t 2 . How long was the rocket in the air before it returned to the ground? 3.75 s
Chapter 8
34
Glencoe Algebra 1
Companies, Inc.
The McGraw-Hill division of Glencoe/McGraw-Hill, a Copyright ©
NAME
8-5
DATE PERIOD
1.
According to legend, Galileo dropped objects of different weights from the so-called “leaning tower” of Pisa while developing his formula for free falling objects. The relationship that he discovered was that the distance d an object falls after t seconds is given by d = 16 t 2 (ignoring air resistance). This relationship can be found in the equation h = 4 t 16 t 2 , where h is the height of an object thrown upward from ground level at a rate of 32 feet per second. Solve the equation for h = 0. t = 0.25 and 0
4.
Your vertical jump height is measured by subtracting your standing reach height from the height of the highest point you can reach by jumping without taking a running start. Typically, NBA players have vertical jump heights of up to 34 inches.
If an NBA player jumps this high, his height h in inches above his standing reach height after t seconds can be modeled by h = 162 t 192 t 2 . Solve the equation for h = 0 and interpret the solution. Round your answer to the nearest hundredth. t = 0 and t ≈ 0.844; The player lands after about 0.84 second.
2.
The area A of a rectangular swimming pool is given by the equation A = 12 w w 2 , where w is the width of one side. Write an expression for the other side of the pool. 12 w
5.
Conner tosses a dog treat upward with an initial velocity of 13.7 meters per second. The height of the treat above the dog’s mouth h in meters after t seconds is given by h = 13.7
t - 4.9
t 2 .
a. Assuming the dog doesn’t jump, after how many seconds does the dog catch the treat? 2.795
3.
Unique Building
Company is constructing a triangular roof truss for a building. The workers assemble the truss with the dimensions shown on the diagram below. Using the
Pythagorean Theorem, find the length of the sides of the truss. 3 yd, 4 yd, 5 yd
b. The dog treat reaches its maximum height halfway between when it was thrown and when it was caught. What is its maximum height? 9.6 m
2 x - 1 yd x yd x + 1 yd
c. How fast would Connor have to throw the dog treat in order to make it fly through the air for 6 seconds? at 29.4 m/s
Chapter 8
35
Glencoe Algebra 1