Factoring Worksheet With Examples Page 46
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50Mixed Problem Solving
For mixed problem-solving practice,
see page 751.
2
Factoring Trinomials: x
+ bx + c
8–3
(pp. 434–439)
2
Factor each trinomial.
Example 5
Factor x
- 9x + 20.
2
2
32. y
+ 7y + 12
33. x
- 9x - 36
b = -9 and c = 20, so m + n is negative and
2
2
34. b
+ 5b - 6
35. 18 - 9r + r
mn is positive. Therefore, m and n must both
be negative. List the negative factors of 20, and
Solve each equation. Check the solutions.
look for the pair of factors with a sum of -9.
2
36. y
+ 13y + 40 = 0
2
37. x
- 5x - 66 = 0
Factors of 20
Sum of Factors
-
1, -20
-21
38.
SOCCER
In order for a town to host an
-
-2,
10
-12
international soccer game, its field’s
-4,
-5
-9
length must be 110–120 yards, and its
width must be 70–80 yards. Green
The correct factors are -4 and -5.
Meadows soccer fi eld is 30 yards
2
longer than it is wide. Write an
x
- 9x + 20 = (x + m)(x + n)
Write the pattern.
expression for the area of the
= (x
-
4)(x
-
5)
m = -4 and
rectangular fi eld. If the area of the
n = -5
fi eld is 8800 square yards, will Green
Meadows be able to host an
international game? Explain.
2
8–4
Factoring Trinomials: ax
+ bx + c
(pp. 441–446)
2
Factor each trinomial, if possible. If the
Example 6
Factor 12x
+ 22x - 14.
trinomial cannot be factored using
2
2
12x
+ 22x - 14 = 2(6 x
+ 11x - 7)
Factor.
integers, write prime.
2
2
39. 2a
- 9a + 3
40. 2m
+ 13m - 24
So, a = 6, b = 11, and c = -7. Since b is
2
2
positive, m + n is positive. Since c is
41. 12b
+ 17b + 6
42. 3n
- 6n - 45
negative, mn is negative. So either m or n is
negative. List the factors of 6(-7) or -42,
Solve each equation. Check the solutions.
where one factor in each pair is negative.
2
2
43. 2r
- 3r - 20 = 0 44. 40x
+ 2x = 24
The correct factors are -3 and 14.
45.
BASEBALL
Victor hit a baseball into the
2
2
+ 11x - 7 = 6x
+ mx + nx - 7
6x
air that modeled the equation
2
= 6x
-
3x + 14x - 7
2
h = -16 t
+ 36t + 1, where h is the
2
height in feet and t is the time in
= (6x
- 3x) + (14x - 7)
seconds. How long was the ball in the
= 3x(2x - 1) + 7(2x - 1)
air if Casey caught the ball 9 feet above
= (2x - 1)(3x + 7)
the ground on its way down?
Thus, the complete factorization of
2
12x
+ 22x - 14 is 2(2x - 1)(3x + 7).
463
Chapter 8 Study Guide and Review
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education