Name———————————————————————— Lesson
Lesson 2.4
2.4
Date —————————————
Practice B
For use with the lesson “Factor and Solve Polynomial Equations”
Factor the sum or difference of cubes.
1. x 3 1 125
2. y 3 2 8
3. 64n3 2 27
4. 27g 3 1 343
5. 2w 3 1 54
6. 40v 3 2 625
Factor the polynomial by grouping.
7. r 3 2 3r 2 1 6r 2 18
8. x 3 1 6x 2 1 7x 1 42
9. c 3 1 4c 2 2 9c 2 36
10. z 3 2 2z 2 2 16z 1 32
11. 25p3 2 25p 2 2 p 1 1
12. 9m3 1 18m 2 2 4m 2 8
Factor the polynomial in quadratic form.
13. x 4 2 36
14. c 4 2 81
15. x 4 1 x 2 2 20
16. 6y 6 2 5y 3 2 4
17. x 6 2 4
18. d 4 2 7d 2 1 10
19. 24q 3 2 81
20. a6 1 7a3 1 6
21. 24x 4 1 26x 2 2 30
22. 2b4 1 14b 3 2 16b 2 112
Find the real-number solutions of the equation.
23. n4 1 6n3 5 0
24. 4k 3 5 9k 2
25. x 3 1 2x 2 2 25x 2 50 5 0
26. 6w 3 1 30w 2 2 18w 2 90 5 0
27. y 4 2 14y 2 1 45 5 0
28. 3r 5 1 15r 3 2 18r 5 0
29. Write a binomial that can be factored either as the difference of two squares or as the
difference of two cubes. Show the complete factorization of your binomial.
30. City Park You are designing a marble planter for a city park. You want the length of the planter
to be six times the height, and the width to be three
times the height. The sides should be one foot thick.
Because the planter will be on the sidewalk, it does
not need a bottom. What should the outer dimensions
of the planter be if it is to hold 4 cubic feet of dirt?
2-40
Algebra 2
Chapter Resource Book
x
3x
6x
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Factor the polynomial completely.
22. 2(b 1 7)(b 2 2)(b 2 1 2b 1 4) 23. 26, 0
Teaching Guide
27. 23, 2​Ï 5, ​ ​Ï 5 ​ , 3 28. 21, 0, 1
1. (x)(x 1 8)(x 2 2) 5 96; The factors should be
set to zero in order to use the zero product property.
2. x3 1 6x2 2 16x 2 96 5 0
3. x2(x 1 6); 216(x 1 6); both have (x 1 6) as a
factor 4. (x 1 4)(x 2 4)(x 1 6) 5 0; 4, 24, and
26; 4; 12 cm by 2 cm by 4 cm
Practice Level A
1. 4x 3 2. 2 3. 8x 4. 16n2 5. 5p2 6. 1 7. C
8. D 9. F 10. A 11. E 12. B
13. (s 2 1)(s 2 1 s 1 1) 14. (q 1 1)(q 2 2 q 1 1)
15. (x 2 3)(x 2 1 3x 1 9)
16. (a 1 5)(a2 2 5a 1 25)
17. (h 1 4)(h2 2 4h 1 16)
18. (2y 2 5)(4y 2 1 10y 1 25)
19. (x2 1 3)(x 1 2) 20. (z2 1 5)(z 2 1)
21. ( f 2 1 1)( f 1 4) 22. (m2 1 4)(m 2 2)
23. (x 3 1 3)(2x 2 1) 24. (t 2 2)(t 1 3)(t 2 3)
25. 0, 3 26. 25, 0 27. 2, 3 28. 24, 4
29. 0, 3 30. 23, 21, 3 31. C 32. A 33. B
Practice Level B
1. (x 1 5)(x 2 2 5x 1 25)
}
}
29. Sample answer: x 6 2 1;
(x 1 1)(x 2 1)(x 2 1 x 1 1)(x 2 2 x 1 1)
30. 6 ft by 3 ft by 1 ft
Practice Level C
1. (x 2 8)(x 2 1 8x 1 64)
2. 2(a 1 6)(a 2 2 6a 1 36)
3. 7(h 1 4)(h2 2 4h 1 16)
4. 23(c 2 2)(c 2 1 2c 1 4)
5. (6x 2 1 1)(2x 2 1) 6. (3k 3 2 7)(k 1 9)
7. (n 1 4)(n 2 4)(3n 2 10)
8. x 3(x 1 1)2(x 2 1) 9. ( y 2 1 9)( y 1 3)(y 2 3)
10. 2(z 2 1 25)(z 1 5)(z 2 5)
11. (3a 2 2 1)(2a 2 1 5)
12. (6b 2 1 7)(b 1 2)(b 2 2)
13. (r 2 1)(r 2 1 r 1 1)(r 2 1 1)
14. 24w 2(w 2 1 2)(w 2 1 1)(w 1 1)(w 2 1)
15. (a 2b 1 5)(a 4b 2 2 5a 2b 1 25)
2
16. (c 2 2 d 2)(2a 2 5b) 17. 210 18. }
​ 3 ​ 19. 4
}
}
3
20. 24, 23, 3 21. 2​ } ​, 1 22. 2​Ï 7 ​,  22, 2, Ï
​
7 ​ 
5
4. (3g 1 7)(9g 2 2 21g 1 49)
1 1
23. 2​ } ​, }
​   ​ 24. 22, 2 25. 21, 0, 1
3 3
}
}
3
​Ï 6 ​  ​Ï 6 ​ 
3
3
26. 21, 2​ } ​, 0, ​ } ​, 1 27. 2​ }   ​, 0, }
​ 
   ​ 28. 0, }
​ 2 ​
4
2
4
2
5. 2(w 1 3)(w 2 2 3w 1 9)
29. Sample answer:
6. 5(2v 2 5)(4v 2 1 10v 1 25)
7. (r 2 1 6)(r 2 3) 8. (x 2 1 7)(x 1 6)
10. (z 1 4)(z 2 4)(z 2 2)
x 4 1 5x 3 1 x 1 5; (x 1 5)(x 1 1)(x2 2 x 1 1)
30. a. V1 5 18πx 3, V2 5 8πx 3, V3 5 2πx 3
b. 28πx 3 5 448π c. about 2.5 d. level 1: 15 ft,
2.5 ft; level 2: 10 ft, 2.5 ft; level 3: 5 ft, 2.5 ft
11. (5p 1 1)(5p 2 1)( p 2 1)
Study Guide
2. (y 2 2)( y 2 1 2y 1 4)
3. (4n 2 3)(16n2 1 12n 1 9)
9. (c 1 3)(c 2 3)(c 1 4)
A24
}
}
9
24. 0, }
​ 4 ​ 25. 25, 22, 5 26. 25, 2​Ï 3 ​,  ​Ï 3 ​ 
12. (3m 1 2)(3m 2 2)(m 1 2)
1. 7x 2(x 2 2)(x 2 1 2x 1 4)
13. (x 2 2 6)(x 2 1 6) 14. (c 1 3)(c 2 3)(c2 1 9)
2. 2(4y 2 1 1)(16y 4 2 4y 2 1 1)
15. (x 1 2)(x 2 2)(x 2 1 5)
3. (x 1 2)(x 2 2)(x 2 3)
16. (2y 3 1 1)(3y 3 2 4) 17. (x 3 1 2)(x 3 2 2)
18. (d 2 2 5)(d 2 2 2)
19. 3(2q 2 3)(4q 2 1 6q 1 9)
20. (a 3 1 6)(a 1 1)(a 2 2 a 1 1)
21. 22(2x 2 2 3)(x 2 2 5)
4. (y 2 3)(y 1 3)(y 1 7) 5. 3b 2(b 2 1 1)2
Algebra 2
Chapter Resource Book
}
6. (z 2 1 4)(z 2 1 2)(z 2 2 2) 7. 61, 6​Ï 2 ​ 
}
}
}
8. 0, 6​Ï 6 ​,  6​Ï 2 ​  9. 0, 6​Ï 3 ​,  63
10. 8 in. by 3 in. by 1 in.
Interdisciplinary Application
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answers
Lesson 2.4 Factor and Solve
Polynomial Equations