Factoring Worksheet With Examples Page 42
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50Solve each equation. Check the solutions.
2
2
24. 3 x
+ 24x + 48 = 0
25. 7 r
= 70r - 175
2
2
26. 49 a
+ 16 = 56a
27. 18 y
+ 24y + 8 = 0
_
_
_
_
2
1
4
4
2
2
28. y
29. a
-
y +
= 0
+
a +
= 0
3
9
5
25
2
2
30. x
31. (w + 3 )
+ 10x + 25 = 81
= 2
2
2
32. p
+ 2p + 1 = 6
33. x
- 12x + 36 = 11
34.
FORESTRY
The number of board feet B that a log will yield can be estimated
_
L
2
by using the formula B =
( D
- 8D + 16), where D is the diameter in
16
inches and L is the log length in feet. For logs that are 16 feet long, what
diameter will yield approximately 256 board feet?
FREE-FALL RIDE
For Exercises 35 and 36, use the following information.
The height h in feet of a car above the exit ramp of an amusement park’s free-fall
2
ride can be modeled by h = -16 t
+ s, where t is the time in seconds after the
car drops and s is the starting height of the car in feet.
35. How high above the car’s exit ramp should the ride’s designer start the drop
in order for riders to experience free fall for at least 3 seconds?
Real-World Link
36. Approximately how long will riders be in free fall if their starting height is
Some amusement park
160 feet above the exit ramp?
free-fall rides can seat
4 passengers across per
coach and reach speeds
37.
HUMAN CANNONBALL
A circus
of up to 62 miles per
acrobat is shot out of a cannon
hour.
with an initial upward velocity
Source:
70 ft
of 64 feet per second. If the
acrobat leaves the cannon
6 ft
6 feet above the ground, will
he reach a height of 70 feet? If
so, how long will it take him to
reach that height? Use the
model for vertical motion.
Factor each polynomial, if possible. If the polynomial cannot be factored,
write prime.
3
2
2
2
2
2
38. 4 a
39. 5 a
+ 3 a
b
+ 8a + 6 b
+ 7a + 6 b
- 4b
2
2
2
2
2
2
4
3
2
2
2
40. x
y
- y
- z
+ x
z
41. 4 m
n + 6 m
n - 16 m
n
- 24m n
3
2
2
3
42.
GEOMETRY
y - 63 y
+ 7 x
- 9x y
The volume of a rectangular prism is x
cubic meters. Find the dimensions of the prism if they can be represented by
binomials with integral coefficients.
EXTRA
43.
GEOMETRY
See pages 734, 751.
If the area of the square
2
- 56x + 49 square
shown is 16 x
inches, what is the area of the
Self-Check Quiz at
rectangle in terms of x?
H.O.T.
Problems
44.
REASONING
Determine whether the following statement is sometimes, always,
or never true. Explain your reasoning.
2
2
2
a
- 2ab - b
= (a - b )
, b ≠ 0
459
Lesson 8-6 Perfect Squares and Factoring
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