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Name ________________________________________ Date __________________ Class__________________
LESSON
14-2
Practice B
Factoring ax2
bx
c
Factor each trinomial.
1. 2x2
13x
15
2. 3x2
________________________
4. 5x2
21x
________________________
7. 7x2
59x
24
11x
13
8. 3x2
29x
12
11. 3x2
7x
12
14. 11x2
12x2
35x
18
________________________
15
9. 8x2
2x
12. 2x2
16
25x
24
17. 9x2
49x
30
20x2
29x
6
_________________________
22. The area of a rectangle is 20x2 27x 8.
The length is 4x 1. What is the width?
20
73x
9
17x
30
________________________
15. 9x2
3x
2
________________________
18. 6x2
_________________________
20.
23x
________________________
_________________________
________________________
19.
14x
27
________________________
_________________________
________________________
16. 12x2
6. 6x2
7
_________________________
________________________
13. 8x2
11x
24x
________________________
________________________
________________________
10. 2x2
3. 4x2
8
_________________________
5. 4x2
4
10x
x
40
________________________
21.
2x2
5x
42
________________________
_________________________
© Houghton Mifflin Harcourt Publishing Company
386
Holt McDougal Analytic Geometry
6.
Problem Solving
20; 1
Sum
1. x
1 and 20
19
2. rug: (x 5)(x 4); wall: (x 2)(x 15);
rug: 16 ft by 25 ft, wall: 22 ft by 35 ft
2 and 10
8
Factors
4 and
(x
7.
4)(x
5
3. a. x 5
b. 12 in. by 19 in.
c. x2 x 12
1
4. D
5)
Factors
Sum
1 and
4
3)(x
6)
10. (x
5)(x
9)
Reading Strategies
3
2 and 2
1)(x 4)
8. (x
0
9. (x
7)(x
2)
1
2
1
3
1 1
2 3
1
3
3. 6 x
1 3
2 3
1
2
1
3
2
2
3 2
2 3
2 x
1
2
3 x
6. 28 x
7. 6 x
8. 12 x
x
1
7
x
4
3
5
3
x
x
3.
;
4.
:
5.
;
6.
;
7.
;
8.
;
9.
;
8)(x
3)
10. (x
3)(x
7)
12. (x
6)(x
5)
6x 2
3x
6x 2
5x 1
2x 1
1
3
3)(2x
5)
4. (3x
2)(2x
5)
6. (2x
3)(4x
1)
8. (3x
7)(3x
2)
1)(4x
7. (4x
1)(x
9. (3x
5)(2x
5)
10. (5x
2)(x
11. (7x
5)(3x
1)
12. (4x
3)(3x
13. (5x
9)(2x
1)
14. (3x
4)(x
1)
16. (4x
3)(x
3)
18. (3x
4)(2x
15. (x
2)(5x
17. (2x
19. (5x
1)(2x
2
48x
4)
2. (2x
5. (2x
7)
8)
3)
7)
27); (5x
20.
1 (2x
1)(3x
4)
21.
1(5x
2)(4x
3)
3)(x
9)
22. 4x
1
4)
4)
5)
Practice B
1
4
2. (3x
4)(x
2)
4. (5x
1)(x
4)
1)
6. (3x
4)(2x
3)(x
8)
8. (3x
5)(x
9. (8x
1)(x
9)
10. (2x
13)(x
1)
11. (3x
8)(x
2)
12. (x
10)(2x
3)
13. (x
4)(8x
3)
14. (x
3)(11x
8)
16. (4x
3)(3x
4)
5
2
7
4
2)
c
5)(x
1
3
4. Yes; the given polynomial expression is
written as a product of polynomials of
lower degree. There is no requirement
that the coefficients be integers.
1
5
;
3. (3x
5
6
(2 x 1)(3 x 1)
5. 15 x
2.
Practice A
1. 1; (x 3)(5x
1
,
6
1
3
x
;
14-2 FACTORING ax2 bx
1. Distributive Property
1
2
1.
11. (x
Challenge
2.
5. J
6. B
4; 3
(x
8m
1. (2x
3)(x
3. (2x
9)(2x
5. (4x
7)(x
7. (7x
15. (3x
1)(3x
5)
3)
2)
5)
3)
© Houghton Mifflin Harcourt Publishing Company
A72
Holt McDougal Analytic Geometry
17. (9x
5)(x
6)
18. (3x
19. 1(4x
9)(3x
20. 1(5x
21. 1(2x
6)(4x 1)
7)(x 6)
22. 5x
Problem Solving
1. (x 3) cm
2.
1)(8c
5. (6m
1)
2. (7x
3)(2x
3)
5)
4. (4b
5)(5b
1)
6. (2x
7)(3x
4)
5)(2m
7. 1(5x
9. (5f
1(4t 4)(4t 1)
or 4(4t 1)(t 1); 0 feet
3. (3x
8
3. (2c
5)
3)(4x
9)(3f
11. (15a
9)
8)(a
1(2x
7)(4t
10. (16h
50)(2x
15. (3k
4)(3k
17. (7x
4)(3x
5. C
6. F
7. B
8. G
Reading Strategies
7)
5)(4h
3)
1. 1 3
2. 1 12; 2 6; 3 4
5)
3)
14. (4x
5)(x
2)
16. (8n
11)(3n
4)
18. (6p
7)(3p
25)(w
3) ft; increase of 2 ft
4. length increased by 5 ft,
width increased by 7 ft
4)
9)(2x
1(13w
8. (t
2)
13. (3x
19.
5)
2)
Practice C
1. (3d 7)(2d
12.
8)(2x
3. minus, minus
2)
4. (
2)
x
)(
x
)
5. Possible answer:
2)
1)
( x
)( x
)
Outer
20. (12x
5)(x
6)
3
1 1
12 3
21. (3y
1)(4y
15)
3
12 1
Inner
12
1 1
37 No
1 3
1
12 1
15 No
22. 4x
5
3
4 1
3 3
3
4 1
13 No
23. 2x
9 inches
3
3 1
4 3
4
3 1
15 No
3
6 1
2 3
2
6 1
12 No
3
2 1
6 3
6
2 1
20 Yes
Review for Mastery
1.
Factors
Factors
1; 5
1; 4
1; 4; 5; 1; 9
1; 5
4; 1
1; 1; 5; 4; 21
1; 5
2; 2
1; 2; 5; 2; 12
(x
Outer
Inner
6. (3x
2)(x
6)
14-3 FACTORING SPECIAL PRODUCTS
Practice A
2)(5x
2)
1. 5; x; 5
2. (3x
4)(x
1)
2. 1; 3x; 3x; 1; 3x; 2; 1
3. (2x
7)(x
3)
4. (2x
3)(2x
5. (3x
5)(x
4)
6. (5x
1)(x
7.
1(2x
5)(x
1)
3. (x
7)
6. 12x
Challenge
7 15
12 15
4 5 0
3. (6x
1)
5. (x
1)(x
6. (x
4)(2x
2. 3
3
4. (8x
3)(x
1)(x
4. (6x
2)2
5. 6 is not a perfect square
1)
1. 4
9)2
2(2x 6).
7. a. x 4 in.
b. 4(x 4) in.
c. 48 in.
4 32
12 32
8 0
8. 3; 3
10. (t
5)
3
9. 2p; 7; 2p; 7
12)(t
3
12)
11. (4x5
y)(4x5
y)
5)
5)
© Houghton Mifflin Harcourt Publishing Company
A73
Holt McDougal Analytic Geometry
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