Name

Date

Lesson
Practice A
1.4 For use with the lesson Solve ax2 + bx + c = 0 by Factoring

Factor the expression. If the expression cannot be factored, say so.

Lesson 1.4

1. 2x 2 1 5x 1 2 2. 2x 2 1 3x 1 1 3. 3x 2 1 5x 2 2

4. 2x 2 2 3x 1 1 5. 4x 2 1 2x 2 2 6. 6x 2 2 7x 2 3

7. 5x 2 1 x 2 4 8. 9x 2 2 3x 2 6 9. 4x 2 1 13x 1 3

10. 6x 2 1 2x 2 4 11. 4x 2 2 9 12. 4x 2 2 4

13. 2x 2 2 10x 1 12 14. 3x 2 2 9x 2 12 15. 27x 2 2 3

16. 8x 2 2 20x 2 12 17. 8x 2 1 24x 1 18 18. 30x 2 1 5x 2 10

Solve the equation.

19. 2x 2 2 3x 1 1 5 0 20. 2x 2 1 5x 1 3 5 0 21. 6x 2 2 7x 1 2 5 0

22. 3x 2 2 8x 2 3 5 0 23. 4x 2 2 7x 1 3 5 0 24. 4x 2 2 4x 2 15 5 0

25. 2x 2 2 2x 2 12 5 0 26. 6x 2 2 15x 2 9 5 0 27. 12x 2 1 4x 2 8 5 0

Find the zeros of the function by rewriting the function in intercept form.
28. y 5 2x 2 2 6x 1 4 29. y 5 3x 2 1 6x 2 9 30. f (x) 5 5x 2 1 10x 2 40

31. y 5 4x 2 2 12x 1 9 32. g(x) 5 18x 2 2 2 33. y 5 16x 2 1 64x 1 60

Find the value of x.

Copyright Houghton Mifin Harcourt Publishing Company. All rights reserved.

34. Area of the square 5 81 35. Area of the rectangle 5 16

x
3x 1 2
3x

3x

36. Multiple Choice What are all the solutions to 2x 2 1 3x 1 6 5 x 2 1 3x 1 15?

A. 3 B. 23, 3 C. 23 D. 2, 4

37. Pool A pool deck of uniform width is going to be built x ft

around a rectangular pool that is 20 feet long and 15 feet
wide. After the deck is built, a total of 414 square feet
will be occupied. How wide is the deck encompassing 15 ft
the pool?

x ft
20 ft
x ft x ft

Algebra 2
1-46 Chapter Resource Book
 3
Lesson 1.4 Solve ax2 + bx + c 35. 2 36. }
2 37. 0.375 ft
= 0 by Factoring, continued
Practice Level C
24; they are the same.
1. (4x 2 3)(x 2 3) 2. (3x 1 4)(2x 2 7)
19x; they are the same.
3. (5x 1 2)(2x 1 5) 4. (3x 1 4)(3x 1 4)
6. The trinomial and product of binomials in
5. 23(2x 2 3)(2x 1 3) 6. 4(3x 1 2)(x 2 4)
Question 1 are different. The trinomial and
product of binomials in Question 5 are equivalent. 7. 23(5x 1 4)(x 2 1) 8. x(3x 2 1)(2x 2 1)
9. cannot factor 10. x 2(2x 1 3)(2x 1 3)
Practice Level A
11. 3x 2(4x 2 3)(2x 1 3) 12. 4x(6x 2 5)(3x 2 7)
1. (2x 1 1)(x 1 2) 2. (2x 1 1)(x 1 1)
13. (x 2 1 9)(x 2 3)(x 1 3)
3. (3x 2 1)(x 1 2) 4. (2x 2 1)(x 2 1)
14. (2x 2 1 3)(x 2 1 1)
5. 2(2x 2 1)(x 1 1) 6. (3x 1 1)(2x 2 3)
15. 3(2x 2 2 1)(x 2 1)(x 1 1)
7. (5x 2 4)(x 1 1) 8. 3(3x 1 2)(x 2 1)
1 5 3 3 1
9. (4x 1 1)(x 1 3) 10. 2(3x 2 2)(x 1 1) 3, 3 17. 1, }
16. } 2 18. 2}4, }
4 19. 21, } 6
11. (2x 1 3)(2x 2 3) 12. 4(x 2 1)(x 1 1) 4 3 3 7 4 7 3 5
20. 2}, } 21. 2}, } 22. 2}, }
23. 2}4, }
7
13. 2(x 2 2)(x 2 3) 14. 3(x 1 1)(x 2 4) 3 2 2 9 3 4
15. 3(3x 2 1)(3x 1 1) 16. 4(2x 1 1)(x 2 3) 2 2 2 7 3
24. 2}, 4 25. 1, 2 26. 2}, 2 27. }, }
28. }
2
5 3 3 5
17. 2(2x 1 3)(2x 1 3) 18. 5(3x 1 2)(2x 2 1)
29. 10 30. 99x 2 1 2900x 2 38,900 5 0; 100 ft
1 3 1 2 1
2, 1 20. 2}2, 21 21. }
19. } 2, }
3 22. 2}3, 3 Study Guide
3 3 5 1 1. 2(x 2 6)(x 2 1) 2. 3(x 1 1)(x 1 7)
23. }, 1 24. 2}, } 25. 22, 3 26. 2}, 3
4 2 2 2 3. 6(x 2 3)(x 2 4) 4. 4(x 2 2)(x 1 3)
2 5. 5(x 1 1)(x 2 5) 6. 3(x 2 6)(x 1 2)
27. 21, } 3 28. 1, 2 29. 23, 1 30. 24, 2
3

Copyright Houghton Mifin Harcourt Publishing Company. All rights reserved.

3 1 1 5 3 7. x 56} 8. x 5 2 9. x 5 21, x 5 4
31. } 32. 2}, } 33. 2}, 2} 5
2 3 3 2 2
10. The length is 6 in. 11. The shop should
34. 3 35. 2 36. B 37. 1.5 ft charge $60/bike to maximize weekly revenue of
Practice Level B $3240.
1. (3x 2 2)(x 1 4) 2. (2x 2 1)(x 1 3) Interdisciplinary Application
3. (2x 1 1)(2x 1 1) 4. cannot factor 1. about 210 yd 2. about 60 yd
5. (4x 2 3)(x 1 2) 6. (2x 1 5)(x 1 3) 3. about 287 yd 4. about 361 yd
7. (3x 1 2)(3x 1 2) 8. 3(2x 2 3)(2x 2 1) Challenge Practice
9. 2(3x 2 1)(3x 1 1) 10. (4x 1 3)(3x 1 2) 1. Sample answer: c 5 23, (2x 2 1)(x 1 3);
11. (5x 2 4)(3x 1 4) 12. cannot factor c 5 212, (2x 2 3)(x 1 4)
13. 3(4x 2 1)(x 2 3) 14. (6x 2 7)(3x 1 2) 2. Sample answer: c 5 28, (3x 1 2)(x 2 4);
15. 2(5x 2 6)(2x 2 3) 16. 7(3x 1 1)(2x 1 1) c 5 225, (3x 1 5)(x 2 5)
17. (212x 1 11)(x 1 1) 18. 4(5x 1 3)(4x 1 1) 3. (22, 23), } 1
4 11
3, } 2
3
1 3 1 3 2 2
19. 22, } 2 20. 2}2, 3 21. } 2, } 2 22. 2}3, } 3
1
3
4. 2} 2
2, 24 , (3, 23)
1 1 4 5 2 1 3
4, }
23. } 2 24. 2}3 25. 2}3, 2}3 26. 2}2, } 2 5. (2n 2 2)(2n)(2n 1 2); An even integer is one
that is a multiple of 2. Because n is an integer,
3 3 3 2 3 5
27. 0, } 7 28. } 8, }
4 29. 2}3, 0 30. 2}2, } 6 2n is an even integer. You can add and subtract 2
from 2n to obtain a set of three consecutive even
6 4 8
31. 2, 3 32. 2}, } 33. 2} , 1 34. none integers. 6. 5 7. 24 club members
5 5 11

Algebra 2
A8 Chapter Resource Book