Factoring Worksheet With Examples Page 13
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50Solve each equation. Check the solutions.
21. x(x - 24) = 0
22. a(a + 16) = 0
23. (q + 4)(3q - 15) = 0
24. (3y + 9)(y - 7) = 0
25. (2b - 3)(3b - 8) = 0
26. (4n + 5)(3n - 7) = 0
2
2
27. 3 z
+ 12z = 0
28. 2 x
= 5x
29.
BASEBALL
Malik popped a ball straight up with an initial upward velocity
of 45 feet per second. The height h, in feet, of the ball above the ground is
2
modeled by the equation h = 2 + 48t - 16 t
. How long was the ball in the
air if the catcher catches the ball when it is 2 feet above the ground? Is
your answer reasonable in the context of this situation?
30.
MARINE BIOLOGY
In a pool at an aquarium, a dolphin jumps out of the
water traveling at 20 feet per second. Its height h, in feet, above the water
2
after t seconds is given by the formula h = 20t - 16 t
. Solve the equation
for h = 0 and interpret the solution.
Factor each polynomial.
2
2
2
3
2
2
3
31. 12 x
32. 18 a
y
z + 40x y
z
b c
- 48ab c
Real-World Career
Marine Biologist
GEOMETRY
Find an expression for the area of a square with the
A marine biologist uses
given perimeter.
math to study and
analyze factors that
33. P = (12x + 20y) in.
34. P = (36a - 16b) cm
affect organisms living in
and near the ocean.
_
_
3
1
2
35.
GEOMETRY
The expression
n
-
n can be used to find the number of
2
2
diagonals in a polygon that has n sides. Write the expression in factored
For more information,
form and find the number of diagonals in a decagon (10-sided polygon).
go to
.
SOFTBALL
For Exercises 36 and 37, use the following information.
Alisha is scheduling the games for a softball league. To find the number of
_
_
1
1
2
games she needs to schedule, she uses the equation g =
-
n
n, where g
2
2
represents the number of games needed for each team to play each other
exactly once and n represents the number of teams.
36. Write this equation in factored form.
37. How many games are needed for 7 teams to play each other exactly
3 times?
GEOMETRY
Write an expression in factored form for the area of each
shaded region.
38.
39.
EXTRA
See pages 733, 751.
Self-Check Quiz at
2
H.O.T.
Problems
40.
REASONING
Represent 4 x
+ 12x as a product of factors in three different
ways. Then decide which of the three is the completely factored form.
Explain your reasoning.
430
Chapter 8 Factoring
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