Factoring Worksheet With Examples Page 35
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5038.
REASONING
The following statements appear to prove that 2 is equal to 1.
Find the flaw in this “proof.”
Suppose a and b are real numbers such that a = b, a ≠ 0, b ≠ 0.
(1)
a = b
Given.
2
(2)
a
= ab
Multiply each side by a.
2
2
2
- b
= ab - b
2
(3)
a
Subtract b
from each side.
(4) (a - b)(a + b) = b(a - b)
Factor.
(5)
a + b = b
Divide each side by a - b.
(6)
a + a = a
Substitution Property; a = b
2a = a
(7)
Combine like terms.
(8)
2 = 1
Divide each side by a.
Writing in Math
39.
Use the information about basketball on page 447 to
explain how to determine a basketball player’s hang time. Include a
maximum height that is a perfect square and that would be considered a
reasonable distance for a student athlete to jump. Describe how to find the
hang time for this height.
40. What are the solutions to the
41.
REVIEW
Carla’s Candle Shop sells
2
quadratic equation 25 b
- 1 = 0?
3 small candles for a total of $5.94.
Which expression can be used to find
_
1
A 0,
the total cost c of x candles?
5
_
5.94
_
1
F
B -
, 0
x
5
G 5.94x
_
1
, 1
C
_
x
H
5
1.98
_
_
1
1
D -
,
J 1.98x
5
5
Factor each trinomial, if possible. If the trinomial cannot be factored using
integers, write prime.
(Lesson 8-4)
2
2
2
42. 2 n
+ 5n + 7
43. 6 x
- 11x + 4
44. 21 p
+ 29p - 10
Solve each equation. Check the solutions.
(Lesson 8-3)
2
2
2
45. y
+ 18y + 32 = 0
46. k
- 8k = -15
47. b
- 8 = 2b
48.
STATISTICS
Amy’s scores on the first three of four 100-point biology tests
were 88, 90, and 91. To get a B+ in the class, her average must be between
88 and 92, inclusive, on all tests. What score must she receive on the fourth
test to get a B+ in biology?
(Lesson 5-4)
PREREQUISITE SKILL
Find each product.
(Lesson 7-7)
2
2
49. (x + 1)(x + 1)
50. (x + 8 )
51. (3x - 4)(3x - 4)
52. (5x - 2 )
452
Chapter 8 Factoring
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