Chapter 6 Answers
22. -5, 0, 2;
Practice 6-1
3
2
y
1. y = -0.0439814815x + 0.6507936508x - 2.935185185x
+ 24.84126984; 21.098 2. y = 0.0130787037x3 -
0.1743055556x2 + 0.7951058201x + 3.125396825; 4.6362
3. 5x + 2; linear binomial 4. -3; constant monomial
5. 6x4 - 1; quartic binomial 6. 5s4 - 2s + 1; quartic
trinomial 7. 2m2; quadratic monomial 8. -4x3 + x2 + 3x;
cubic trinomial 9. 2x2 - 1; quadratic binomial 10. -3m3
+ 5m2; cubic binomial 11. -7x2 + 5x; quadratic binomial
12. 3x3; cubic monomial 13. -x3 + 2; cubic binomial
14. -x; linear monomial 15. a5 + a4 + a3; quintic trinomial
16. x2 - 25; quadratic binomial 17. p2 - 5p + 6;
quadratic trinomial 18. 9c4; quartic monomial
19. b - 3; linear binomial 20. 12x - 6; linear binomial
21. s2 1 32 ; quadratic binomial 22. 21 x4 1 x 2 54 ; quartic
trinomial 23. 21 z5 1 1; quintic binomial 24. 3x + 5 units
3
25. 0.000204x3 + 0.2617908x2 - 3.6243065x + 29.3053733;
about $955.82
26. 0.0000006x3 - 0.0005101x2 + 0.1270416x + 2.0612682;
about 12 yr
Practice 6-2
1. 5, multiplicity 3 2. 0; 8, multiplicity 2 3. 2; -7, multiplicity
3 4. 0, multiplicity 2; 4, multiplicity 2 5. -3, 0, 3
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6. 252 ; 3, multiplicity 2 7. y = 2x3 - x2 - 50x + 25
8. y = -2x3 + 15x2 - 22x - 15
9. V = x3 + 54x2 + 936x + 5184
10. y = x3 - 6x2 + 5x + 12
11. y = x3 - 4x2 + 5x - 2 12. y = x4 - 2x3 - 15x2
13. y = x3 + 6x2 + 12x + 8 14. x3 - 2x2 + x
15. x3 + 7x2 + 15x + 9
16. 2x4 + 23x3 + 60x2 - 125x - 500
17. y = 2x(x + 2)(x + 3)
18. y = x2(x + 2)(x - 3) 19. y = -3x(x - 3)2
20. -1, 1, 3;
y
2
(1, 0)
2
(1, 0) x
2 (3, 0)
O
(5, 0) (0, 0)
4 O
(2, 0)
4
x
23. rel. max.: 4.06; rel. min.: -8.21; zeros: 0, 2, 5
24. rel. max.: 16.9; rel. min.: -5.05; zeros: -3, 1, 3
25. x(x + 2)(x - 8) 26. x(x + 3)(x + 4)
27. x(x - 3)(x - 5) 28a. V = x2(20 - x)
28b. about 1185 in. 3
Practice 6-3
1. yes 2. yes 3. no 4. yes 5. x2 - 3x + 2
6. x2 + 3x - 7, R 5 7. -2x2 + 9x + 5 8. x2 + 6x + 9
9. x2 - x + 8, R -12 10. x2 - 7, R -10 11. x3 + x, R 1
12. x3 + 2x2 + 6 13. x3 - x2 + x + 11, R 32
14. 2x3 + 15x2 - 125 15. -1 16. -13 17. 0 18. 39
19. x - 16 20. 2x + 11, R 48 21. x2 + 6x + 3, R 2
22. 3x2 - 7x + 7, R -8 23. (x + 1)(x - 3)(x + 5)
24. (x - 2)(x + 3)(x - 4) 25. 2x2 - 2x - 1, R 16
26. x3 + 3x2 + 3x + 4, R 1 27. x3 + 2x2 - x, R 1
28. x4 + x3 + x2 + x + 1 29. x3 + 2x2 + x + 2, R -6
30. 3x2 - 3x + 3 31. width: x - 3; height: x - 5
Practice 6-4
1. (2x - 3)(4x2 + 6x + 9); 23 ,
23 4 3i"3
4
2. (x + 4)(x2 - 4x + 16); -4, 2 4 2i"3
3 4 3i"3
3. 2(x + 3)(x2 - 3x + 9); -3,
2
4. 2(x - 5)(x2 + 5x + 25); 5,
25 4 5i"3
2
5. 4(x - 2)(x2 + 2x + 4); 2, 21 4 i"3
1 4 i"3
6. (3x + 1)(9x2 - 3x + 1); 213 ,
6
7. (4x - 1)(16x2 + 4x + 1); 41 ,
21 4 i"3
8
8. (x - 3)(x2 + 3x + 9); 3,
21. -2, 3;
2
10
23 4 3i"3
2
9. (x + 1)(x - 1)(x + 2)(x - 2); -2, -1, 1, 2
2
(2, 0)
20
y (3, 0) x
O
2
2
4
6
Algebra 2 Chapter 6
10. (x + 1)(x - 1)(x2 - 11); -1, 1, 2"11, "11
11. (x2 - 2)(x2 - 8); 2"2, "2, 2"8, "8
12. (x + 2)2(x - 2)2; -2, 2
13. (x2 - 7)(x2 - 2); 2"7, "7, 2"2, "2
14. (x2 + 4)(x2 + 9); -2i, 2i, -3i, 3i
15. (x + 1)(x - 1)(x + 3)(x - 3); -1, 1, -3, 3
16. (x + 1)(x - 1)(x2 + 4); -1, 1, -2i, 2i
17. 5.52% 18. -2, 2, -0.71, 0.71 19. 0.06, 15.94 20. 0
Answers
39
(continued)
21. -0.59, 0, 0.42 22. -0.67, 0, 1.4 23. -9, 0, 9
24. (n - 1)n(n + 1) = -336; -8, -7, -6
25. (x - 5)(x2 + 5x + 25) 26. (x2 - 3)(x2 - 5)
27. (x + 1)(x - 1)(x2 + 2) 28. (x + 1)(x2 - x + 1)
29. (x2 - 6)(x2 + 4) 30. (x2 + 1)(x2 + 9)
31. (x + 3)(x2 - 3x + 9) 32. (x2 - 2)(x2 + 9)
21 4 i"3
33. 0, 1,
34. 21, 1, 2"6, "6
2
35. 2"14, "14, 2i, i 36. 2i"2, i"2, 22i"2, 2i"2
37. -3, 3, -3i, 3i 38. 2"5, "5, 2i"5, i"5
39. 0, -2, 2, 2i"3, i"3 40. 0, 2, 6
1
8
4 ,4
3
8
19. 3 20. 4, -3i, 3i 21. 22, 1 4 "7
21 4 i"5
24. -3, 1, 4
2
25. -4, 2i"7, i"7 26. -1, 21 4 i"3 27. -3, 3, -2i, 2i
2 2
28. -2, 2, 2"3, "3 29. 23 , 3 , 2i, i
30. 2"3, "3, 212 i, 12 i
22. 2, 1 4 "5 23. 1,
Practice 6-7
1. 2 2 3i, 2"7 2. 3 1 "2, 1 2 "3 3. 4i, 6 1 i
4. 5 1 "6, 22 2 "10 5. x4 - 8x3 + 21x2 - 32x + 68
6. x4 - 4x3 - x2 + 8x - 2 7. x4 + 3x2 - 54
8. x4 - 6x3 + 9x2 + 6x - 20 9. 4, 2, -1 10. 3, 1, -5
2343"5
11. -4, -3, 21 12. 7, -2, -4 13. 3;
2
1. combination 2. permutation 3. permutation 4. combination 5. 12 6. 66 7. 792 8. 12 9. 1 10. 15 11. 1 12. 84
13. 1 14. 252 15. 2002 16. 2,118,760 17. 40,320 18. 110
19. 17,280 20. 360 21. 479,001,600 22. 239,500,800
23. 95,040 24. 12 25. 3024 26. 455 27. 60 28. 360
29. true, comm. prop. of mult. 30. false; Let a = 2. (22)! =
24 2 4 = (2!)2 31. false, Let a = 2 and b = 3. 2 ? 3! =
12 2 720 = (2 ? 3)! 32. true; identity prop. of add.
33. false; Let a = 2 and b = 3. (2 + 3)! = 120 2 8 =
2! + 3! 34. false; Let a = 2. (2!)! = 2 2 4 = (2!)2
14. -2, -1, 1, 2 15. 2, 2 4 i 16. -1, 3 4 i 17. 1, 2 4 3i
18. -2, 1 4 2i 19. 1, -1, 5 20. -4, 2 21. -2, 1, 3
Practice 6-8
Practice 6-5
22. 10, 21 4 i"19 23. 1, -3 24. 3, 12 , 212
234"13
26. -3, 23 , 214
25. 2,
2
27. 41, 43, 45, 415; none 28.41, 42, 44, 4 12 , 4 13 , 4 23 ,
1 , 4 1 , 4 1 ; -4, 21 , 1
1 1 1 2 4
4 6 9 9 9 12 18 36
6 6
29. 41, 4 12 ;-1, 212 30. 41, 42, 44, 4 12 , 4 13 , 4 23 , 4 43 , 4 41 ,
1
1 1
1
4 , 4 ; none 31. 41, 4 ; ; 1 32. 41, 47, 449; none
6 12
5 5
33. x3 - 7x2 + 17x - 15 = 0 34. x3 - 5x2 + 4x - 20 = 0
35. x3 - 5x2 + 4x + 10 = 0 36. x3 + 7x2 + x + 7 = 0
37. x3 + 4x2 + 16x + 64 = 0 38. x3 - 12x2 + 49x - 78 = 0
4
3
4 ,4 ,4 ,4 ,4 ,4 ,4
Practice 6-6
1. -1, 0, 1 2. -4, 0, 4 3. 213 , 0, 12 4. 212 , 0, 13
5. -1, 21 , 0 6. -5, 0, 5 7. 2; 2 or 0; 41, 43, 4 12 , 4 32
5
8. 2; 2 or 0; 41, 42, 45, 410, 4 13 , 4 23 , 4 53 , 4 10
3
9. 4; 4, 2, or 0; 41, 45, 4 12 , 4 52 10. 3; 3 or 1; 41, 43, 49,
1 3 9 1 3 9
4 , 4 , 4 , 4 , 4 , 4 11. 5; 5, 3, or 1; 41, 43, 45,
2 2 2 4 4 4
1 3 5 15 1 5 1 5
415, 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 12. 3; 3 or 1;
2 2 2
2
3 3 6 6
41, 47 13. 3; 3 or 1; 41, 42, 43, 44, 46, 412
14. 4; 4, 2, or 0; 41, 42, 43, 46, 4 12 , 4 23 15. 5; 5, 3, or 1;
1 3 1 3
41, 42, 43, 46, 4 , 4 , 4 , 4 16. 6; 6, 4, 2 or 0; 41, 42,
2 2 4 4
1 2 3 6 9 18 17. 5; 5, 3, or
43, 46, 49, 418, 4 , 4 , 4 , 4 , 4 , 4
7 7 7 7 7
7
1; 41, 45 18. 5; 5, 3, or 1; 41, 42, 43, 46, 4 1 , 4 3 , 4 1 , 4 3 ,
2 2 4 4
40
Answers
1. x4 + 8x3 + 24x2 + 32x + 16 2. a7 + 14a6 + 84a5
+ 280a4 + 560a3 + 672a2 + 448a + 128 3. x7 + 7x6y
+ 21x5y2 + 35x4y3 + 35x3y4 + 21x2y5 + 7xy6 + y7
4. d9 - 18d8 + 144d7 - 672d6 + 2016d5 - 4032d4
+ 5376d3 - 4608d2 + 2304d - 512 5. 256x8 - 3072x7
+ 16128x6 - 48384x5 + 90720x4 - 108864x3 + 81648x2
- 34992x + 6561 6. x9 - 9x8 + 36x7 - 84x6 + 126x5
- 126x4 + 84x3 - 36x2 + 9x - 1 7. 64x12 - 384x10y2
+ 960x8y4 - 1280x6y6 + 960x4y8 - 384x2y10 + 64y12
8. x35 + 14x30y + 84x25y2 + 280x20y3 + 560x15y4
+ 672x10y5 + 448x5y6 + 128y7 9. about 1%
10a. about 99% 10b. about 95% 10c. about 5%
11. about 3% 12. about 3% 13. about 8%
14. about 0.6% 15. n3 - 9n2 + 27n - 27
16. 16n4 + 64n3 + 96n2 + 64n + 16 17. n5 - 30n4
+ 360n3 - 2160n2 + 6480n - 7776 18. n6 - 6n5
+ 15n4 - 20n3 + 15n2 - 6n + 1 19. 8a3 + 24a2 + 24a
+ 8 20. x8 - 4x6y2 + 6x4y4 - 4x2y6 + y8 21. 32x5 +
240x4y + 720x3y2 + 1080x2y3 + 810xy4 + 243y5
22. 64x12 + 192x10y2 + 240x8y4 + 160x6y6 + 60x4y8
+ 12x2y10 + y12 23. x6 - 3x4y2 + 3x2y4 - y6
24. 16b4 + 32b3c + 24b2c2 + 8bc3 + c4
25. 243m5 - 810m4n + 1080m3n2 - 720m2n3 + 240mn4
- 32n5 26. x18 - 6x15y4 + 15x12y8 - 20x9y12
+ 15x6y16 - 6x3y20 + y24 27. x7 + 7x6 + 21x5 + 35x4
+ 35x3 + 21x2 + 7x + 1 28. x8 + 32x7 + 448x6 +
3584x5 + 17920x4 + 57344x3 + 114688x2 + 131072x
+ 65536 29. x6 - 18x5y + 135x4y2 - 540x3y3
+ 1215x2y4 - 1458xy5 + 729y6 30. x5 + 10x4 + 40x3
+ 80x2 + 80x + 32
31. x10 - 5x8y2 + 10x6y4 - 10x4y6 + 5x2y8 - y10
32. y5 + 15y4 + 90y3 + 270y2 + 405y + 243
33. x12 + 18x10 + 135x8 + 540x6 + 1215x4
Algebra 2 Chapter 6
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Chapter 6 Answers
Chapter 6 Answers
(continued)
+ 1458x2 + 729 34. x7 - 35x6 + 525x5 - 4375x4
+ 21875x3 - 65625x2 + 109375x - 78125
35. x4 - 16x3y + 96x2y2 - 256xy3 + 256y4
Reteaching 6-1
Let x = the years since 1980 and y = the points earned.
Linear: y = -8.533x + 831.48667
Quadratic: y = 1.09767x2 - 30.48635x + 890.02893
Cubic: y = -0.05697x3 + 2.80674x2 - 42.97396x +
900.96698
The cubic model gives the best fit. In 2004, the estimated
diving record is 698.72 points.
Reteaching 6-5
1. x3 - 5x2 + 9x - 5 = 0 2. x3 - 8x2 + 9x + 58 = 0
3. x3 - 15x2 + 73x - 111 = 0 4. x3 + 4x2 - 2x - 8 = 0
5. x3 - 3x2 - 3x + 1 = 0 6. x3 - 6x2 + 6x = 0
7. x3 - 7x2 + 9x - 63 = 0 8. x3 - 7x2 + 11x + 3 = 0
9. x3 + 3x2 + x + 3 = 0 10. x3 - 10x2 + 18x - 16 = 0
11. x3 - x2 + 25x - 25 = 0
12. x3 - 10x2 + 33x - 34 = 0
13. x3 - 3x2 + 16x - 48 = 0 14. x3 - 4x2 + 5x = 0
15. x3 + 5x2 - 15x - 7 = 0
16. x3 + 4x2 - 7x - 28 = 0
Reteaching 6-6
Reteaching 6-2
1. f(x) = x3 - 7x2 + 7x + 15
2. f(x) = x3 - 3x2 - 33x + 35
3. f(x) = x3 + 6x2 - x - 6 4. f(x) = x3 + 3x2 - 4x - 12
5. f(x) = x3 - 6x2 + 11x - 6
6. f(x) = x4 - x3 - 11x2 + 9x + 18
7. f(x) = x3 + 6x2 - 16x 8. f(x) = x3 + 8x2 - 20x
9. f(x) = x3 + 6x2 - x - 6
10. f(x) = x3 + 3x2 - 4x - 12
11. f(x) = x3 + 32 x2 - 4x + 6 12. f(x) = x2 + 13 x - 32
13. f(x) = x3 + 10 x2 - 13 x - 4
3
14. f(x) = x3 + 7x2 + 16x + 12
15. f(x) = x3 - 12x - 16 16. f(x) = x3 - 3x - 2
17. 0, -8, 2 18. 2, -2, 3, -3 19. 3, -3 20. 2 2 , 5 21. 0, 8
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3
22. -4, 4, -1, 1 23. 0, -2, 10 24. 2, -2, -3 25. 2 12 , 5, -3
26. 0, -4, 32 27. 0, "5, 2"5 28. 0, 6, -6
Reteaching 6-3
1. 3x - 5, R 2 2. x2 - x + 3, R -22 3. x + 8, R 32
4. x + 3, R 5 5. x2 - 4x - 1 6. 2x2 + x + 1
7. 2x + 2, R 13 8. x2 - 5x + 15, R -101
9. x - 4, R -2 10. 2x2 - 3x + 10, R -24
Reteaching 6-4
1 4 i"3
3. -3, 3, 22i"2, 2i"2
2
23 4 3i"3
4. -2i, 2i, 2i"5, i"5 5. 0, 3,
2
1 4 i"3
6. 212 ,
7. -i, i, 2i"3, i"3 8. 4, 22 4 2i"3
4
1. 2, 21 4 i"3 2. -1,
3 3 4 3i"3 10. -2, 2, 2"3 "3
,
9. 22 ,
4
11. 2"2, "2, 2i"10, i"10 12. 0, 2, -1 4 i"3
"15 "15
"15 "15
6 "6
13. 2 3 , 3 , 2i 3 , i 3 14. 2 "
,
,-i, i
2
2
15. -i, i, -2i, 2i 16. 22"2, 2"2, -i, i 17. -2, 1 4 i"3
18. 22"2, 2"2, 2i"3, i"3
Algebra 2 Chapter 6
1. 1,
1 4 i"11
2. -5, 4 4 3i 3. 23 , 2"5, "5
2
4. 2, -2i, 2i 5. -1, 1, 2"2, "2 6. -3,
54"33
2
Reteaching 6-7
1. 60,480 2. 120 3. 66 4. 230,230 5. 720 6. 32,760 7. 120
Reteaching 6-8
1. 4; 4; 2; 4; 3; y 2. 3; 3; 3; 2; y 3. 5; 5; 3; 10; 3; 5; z
4. x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5
5. x5 - 5x4y + 10x3y2 - 10x2y3 + 5xy4 - y5
6. 8x3 + 12x2y + 6xy2 + y3 7. x4 + 12x3y + 54x2y2
+ 108xy3 + 81y4 8. x5 - 10x4y + 40x3y2 - 80x2y3
+ 80xy4 - 32y5 9. 32x5 - 80x4y + 80x3y2 - 40x2y3
+ 10xy4 - y5 10. x4 - 12x3y + 54x2y2 - 108xy3
+ 81y4 11. 64x3 - 48x2y + 12xy2 - y3 12. x5 - 5x4
+ 10x3 - 10x2 + 5x - 1 13. 1 - 3x + 3x2 - x3
14. x6 + 3x4 + 3x2 + 1 15. y8 + 4y6a + 6y4a2
+ 4y2a3 + a4
Enrichment 6-1
KF GAUSS
Enrichment 6-2
1. (x
3. (x
5. (x
7. (x
+
-
24)(x - 36) 2. (x - 9)(x - 16)
32)(x + 4) 4. (x - 54)(x + 10)
15)(x + 66) 6. (x - 32)(x - 18)
7)(x + 24) 8. (x - 35)(x + 18)
Enrichment 6-3
READ IT CAREFULLY;
3; 10; 9; 4; 12; 2; 13; 6; 16; 15; 1; 11; 7; 14; 17
Enrichment 6-4
1. 0 2. b + c 3. b = -c 4a. a2 4b. bc 4c. a2 = -b2,
a2 = -c2 5. No; a2 will always be a positive number,
and -b2 and -c2 will always be negative numbers.
Answers
41