Factoring Worksheet With Examples Page 41
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502
b. (x - 3 )
= 5
2
(x - 3 )
= 5
Original equation
x - 3 = ± √ 5
Square Root Property
x = 3 ± √ 5
Add 3 to each side.
Since 5 is not a perfect square, the roots are 3 ± √ 5 . Using a calculator,
the roots are 3 + √ 5 or about 5.24 and 3 - √ 5 or about 0.76.
Interactive Lab
2
2
5
A.
z
+ 2z + 1 = 16
5
B.
(y - 8 )
= 7
Determine whether each trinomial is a perfect square trinomial. If so,
Example 1
factor it.
(p. 455)
2
2
1. y
2. 9 x
+ 8y + 16
- 30x + 10
Factor each polynomial, if possible. If the polynomial cannot be factored,
Example 2
write prime.
(p. 456)
2
2
3. 2 x
4. c
+ 18
- 5c + 6
2
2
5. 8 x
- 18x - 35
6. 9 g
+ 12g - 4
Solve each equation. Check the solutions.
Examples 3, 5
(pp. 456–458)
2
2
7. 4 y
+ 24y + 36 = 0
8. 3 n
= 48
2
2
9. a
- 6a + 9 = 16
10. (m - 5 )
= 13
11.
HISTORY
Galileo showed that objects of different weights fall at the
Example 4
same velocity by dropping two objects of different weights from the
(p. 457)
top of the Leaning Tower of Pisa. A model for the height h in feet of
2
an object dropped from an initial height h
feet is h = -16 t
+ h
, where
0
0
t is the time in seconds after the object is dropped. Use this model to
determine approximately how long it took for objects to hit the ground
if Galileo dropped them from a height of 180 feet.
Determine whether each trinomial is a perfect square trinomial. If so,
HOMEWORK
factor it.
For
See
Exercises
Examples
2
2
12. 4 y
- 44y + 121
13. 2 c
+ 10c + 25
12–15
1
2
2
2
14. 9 n
15. 25 a
+ 49 + 42n
- 120ab + 144 b
16–23
2
24–33
3, 5
Factor each polynomial, if possible. If the polynomial cannot be factored,
34–37
4
write prime.
2
2
2
16. 4 k
- 100
17. 4 a
- 36 b
2
2
18. x
+ 6x - 9
19. 50 g
+ 40g + 8
3
2
2
20. 9 t
+ 66 t
- 48t
21. 20 n
+ 34n + 6
2
2
22. 5 y
23. 18 y
- 90
- 48y + 32
458
Chapter 8 Factoring
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