Factoring Worksheet With Examples Page 45
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Study Guide and Review
Lesson-by-Lesson Review
Monomials and Factoring
8–1
(pp. 420–424)
2
Factor each monomial completely.
Example 1
Factor 68cd
completely.
3
2
11. 28n
12. -33a
b
2
= 4 · 17 · c · d · d
2
68cd
68 = 4 · 17, d
= d · d
2
2
13. 150st
14. -378pq
r
= 2 · 2 · 17 · c · d · d
4 = 2 · 2
Find the GCF of each set of monomials.
2
Thus, 68 cd
in factored form is
15. 35, 30
16. 12, 18, 40
2 · 2 · 17 · c · d · d.
2
2
2
17. 12ab, 4a
b
18. 16mrt, 30m
r
2
5
2
19. 20n
, 25np
Example 2
Find the GCF of 15x
y and
2
2
2
3
45xy
.
20. 60x
y
, 15xyz, 35xz
2
15x
y = 3 · 5 · x · x · y
Factor each number.
21.
HOME IMPROVEMENT
A landscape
architect is designing a stone path to
2
= 3 · 3 · 5 · x · y · y
45xy
Circle the common
cover an area 36 inches by 120 inches.
prime factors.
What is the maximum size square stone
that can be used so that none of the
The GCF is 3 · 5 · x · y or 15xy.
stones have to be cut?
8–2
Factoring Using the Distributive Property
(pp. 426–431)
2
Factor each polynomial.
Example 3
Factor 2x
- 3xz - 2xy + 3yz.
2
22. 13x + 26y
23. a
- 4ac + ab -4bc
2
2x
- 3xz - 2xy + 3yz
2
2
2
24. 24a
b
- 18ab
25. 26ab + 18ac + 32 a
2
= (2x
- 3xz) + (-2xy + 3yz)
26. 4rs + 12ps + 2mr + 6mp
=
x(2x - 3z)
-
y(2x - 3z)
27. 24am - 9an + 40bm - 15bn
=
(x -
y)(2x - 3z)
Solve each equation. Check the solutions.
2
Example 4
Solve x
= 5x. Check the
28. x(2x - 5) = 0
solutions.
2
29. 4x
= -7x
Write the equation so that it is of the form
30. (3n + 8)(2n - 6) = 0
ab = 0.
2
x
= 5x
Original equation
31.
EXERCISE
A gymnast jumps on a
2
trampoline traveling at 12 feet per
- 5x = 0
x
Subtract 5x from each side.
second. Her height h in feet above the
x(x - 5) = 0
Factor using the GCF, x.
trampoline after t seconds is given by
2
the formula h = 12t - 16t
. How long is
x = 0 or x - 5 = 0
Zero Product Property
the gymnast in the air before returning
x = 5
Solve the equation.
to the trampoline?
The roots are 0 and 5. Check by
substituting 0 and 5 for x in the
original equation.
462
Chapter 8 Factoring
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