# Chapter 6 Answers Practice 6-1 1. 2.

```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. 0.0008797x3 + 0.2229900x2 - 3.1465532x + 29.0544437;
26. 0.0000006x3 - 0.0005101x2 + 0.1270416x + 2.0612682;
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
&copy; Pearson Education, Inc., publishing as Pearson Prentice Hall.
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)
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&quot;3
4
2. (x + 4)(x2 - 4x + 16); -4, 2 4 2i&quot;3
3 4 3i&quot;3
3. 2(x + 3)(x2 - 3x + 9); -3,
2
4. 2(x - 5)(x2 + 5x + 25); 5,
25 4 5i&quot;3
2
5. 4(x - 2)(x2 + 2x + 4); 2, 21 4 i&quot;3
1 4 i&quot;3
6. (3x + 1)(9x2 - 3x + 1); 231 ,
6
7. (4x - 1)(16x2 + 4x + 1); 41 ,
21 4 i&quot;3
8
8. (x - 3)(x2 + 3x + 9); 3,
21. -2, 3;
2
10
23 4 3i&quot;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&quot;11, &quot;11
11. (x2 - 2)(x2 - 8); 2&quot;2, &quot;2, 2&quot;8, &quot;8
12. (x + 2)2(x - 2)2; -2, 2
13. (x2 - 7)(x2 - 2); 2&quot;7, &quot;7, 2&quot;2, &quot;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
39
(continued)
35. 2&quot;14, &quot;14, 2i, i 36. 2i&quot;2, i&quot;2, 22i&quot;2, 2i&quot;2
37. -3, 3, -3i, 3i 38. 2&quot;5, &quot;5, 2i&quot;5, i&quot;5
39. 0, -2, 2, 2i&quot;3, i&quot;3 40. 0, 2, 6
1
8
4 ,4
3
8
19. 3 20. 4, -3i, 3i 21. 22, 1 4 &quot;7
21 4 i&quot;5
24. -3, 1, 4
2
25. -4, 2i&quot;7, i&quot;7 26. -1, 21 4 i&quot;3 27. -3, 3, -2i, 2i
2 2
28. -2, 2, 2&quot;3, &quot;3 29. 23 , 3 , 2i, i
30. 2&quot;3, &quot;3, 212 i, 12 i
22. 2, 1 4 &quot;5 23. 1,
Practice 6-7
1. 2 2 3i, 2&quot;7 2. 3 1 &quot;2, 1 2 &quot;3 3. 4i, 6 1 i
4. 5 1 &quot;6, 22 2 &quot;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&quot;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&quot;19 23. 1, -3 24. 3, 12 , 212
234&quot;13
25. 2,
26. -3, 23 , 214
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
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&quot;3
33. 0, 1,
34. 21, 1, 2&quot;6, &quot;6
2
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%
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
&copy; Pearson Education, Inc., publishing as Pearson Prentice Hall.
(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 = -4.22893x + 802.79286
Quadratic: y = 1.08564x2 - 30.28429x + 889.64405
Cubic: y = -0.0184939x3 + 1.75142x2 - 36.20234x +
896.74571
The cubic model gives the best fit. In 2008, the estimated
diving record is 850.22 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
&copy; Pearson Education, Inc., publishing as Pearson Prentice Hall.
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, &quot;5, 2&quot;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&quot;3
3. -3, 3, 22i&quot;2, 2i&quot;2
2
23 4 3i&quot;3
4. -2i, 2i, 2i&quot;5, i&quot;5 5. 0, 3,
2
1 4 i&quot;3
6. 212 ,
7. -i, i, 2i&quot;3, i&quot;3 8. 4, 22 4 2i&quot;3
4
1. 2, 21 4 i&quot;3 2. -1,
3 3 4 3i&quot;3 10. -2, 2, 2&quot;3 &quot;3
,
9. 22 ,
4
11. 2&quot;2, &quot;2, 2i&quot;10, i&quot;10 12. 0, 2, -1 4 i&quot;3
&quot;15 &quot;15
&quot;15 &quot;15
6 &quot;6
13. 2 3 , 3 , 2i 3 , i 3 14. 2 &quot;
,
,-i, i
2
2
15. -i, i, -2i, 2i 16. 22&quot;2, 2&quot;2, -i, i 17. -2, 1 4 i&quot;3
18. 22&quot;2, 2&quot;2, 2i&quot;3, i&quot;3
Algebra 2 Chapter 6
1. 1,
1 4 i&quot;11
2. -5, 4 4 3i 3. 23 , 2&quot;5, &quot;5
2
4. 2, -2i, 2i 5. -1, 1, 2&quot;2, &quot;2 6. -3,
54&quot;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
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.
41
(continued)
1. 41, 42, 43, 46, 47, 414, 421, 442
2.
60
1
3 -34
-42
6
9
1
3. 7, 14, 21, 42
4. -140
1
1
3
-14
-11
54
20
120
78
-34
-42
154 -1680
120 -1722
5. -21, -42 6. 41, 42, 43, -6, -7 7. -7, 24&quot;10
8. 41, 42, 43, 44, 46, 48, 49, 412, 418, 424, 427, 436,
454, 472, 4108, 4216; -3, 2, -6i, 6i; upper: 3, lower: -4
9. 41, 42, 43, 44, 46, 48, 412, 416, 424, 448; -1, 4,
22i&quot;3, 2i&quot;3; upper: 6, lower: -3 10. 41, 42, 43, 44, 45,
46, 48, 49, 410, 412, 415, 416, 418, 420, 424, 430, 436,
440, 445, 448, 460, 472, 480, 490, 4120, 4144, 4180,
4240, 4360, 4720; -9, 5, -4i, 4i; upper: 6, lower: -10
Enrichment 6-6
TEAL; LOON; TERN;
-1, -1 4 i; -2, 1 4 i; -3, 1 4 3i;
3, 4i; 0, 2 4 i; -1, 1 4 3i;
3, 2 4 i; 3, 1 4 i; 3, -1 4 i;
-2, 1 4 3i; -3, 4i; -4, 1 4 3i
Enrichment 6-7
1. 88 2. 84 3. AE 4. 1320 5. 95,040 6. permutations
7a. combinations 7b. order doesn’t matter 7c. 12C3 = 220
8. 12C5 = 792 9a. 12C7 = 792 9b. nCr = nCn-r
or 12C5 = 12C7
Enrichment 6-8
(x + 9y)4
(x + 10y)5
(x + 14y)3
(x + 6y)6
(x + 11y)4
(x + 4y)8
(x + 12y)9
(x + 8y)6
(x + 13y)3
(x + 5y)7
(x + 3y)6
(x + 15y)8
(x + 1y)10
(x + 2y)12
TURING MACHINES
Chapter Project
Activity 1: Graphing
Check students’ work.
42
Activity 2: Analyzing
Check students’ work.
Activity 3: Graphing
Check students’ work.
✔ Checkpoint Quiz 1
1. Answers may vary. Sample: (x + 3)2(x - 2)
2. n = 7m4 + 4m2 - m; quartic trinomial
3. f(t) = 3t3 + 6t - 7; cubic trinomial
4. f(r) = 2r2 + 5r + 7; quadratic trinomial
5. -2, multiplicity 2; 5, multiplicity 4
6. 223 , multiplicity 3; 5, multiplicity 5
7. 0, multiplicity 2; -4, multiplicity 3; 1, multiplicity 1
8. x2 + 4x + 3 9. 2x2 + 5x + 2 10. -74
✔ Checkpoint Quiz 2
1. 0, 212 , 3 2. -4, 2 4 2i&quot;3 3. 3, -3, i, -i
25 4 &quot;29
5. 12 , i&quot;5, 2i&quot;5 6. 2 2 3i, 2&quot;7;
2
Degree 4 7a. 360 7b. 30 7c. 15 7d. 1 8. 2002
9. 72,681,840
Enrichment 6-5
4. -4,
Chapter Test, Form A
1. 3x4 + 6x3 - 2; quartic trinomial 2. 12x2 - 2x;
quadratic binomial 3. 4x3 + 4x2 - 120x; cubic trinomial
4a. y = 0.00001065x3 - 0.000584x2 + 0.02241x + 1.71758
4b. 2.55 million 5. -0.64, 0.64 6. -0.60 7. -0.85, 4.05
8. 2.20 9. -1.57, 1 10. 2.21 11. y = x3 - 10x2
+ 31x - 30 12. y = x3 + x2 - x - 1
13. y = x4 + x2 - 12 14. y = x4 - 4x3 + 20x - 25
15. 1, multiplicity 2; 32 , multiplicity 3 16. -4, multiplicity 2;
2 , multiplicity 5 17. -1; -2, multiplicity 3; 0, multiplicity 2
3
18. -3, -2, 1 19. 0, 2, 8 20. -8, -2, 5 21. -9, 0, 6
22. 2x2 + 3x + 2 23. x2 + 4 24. x2 + 5x + 6
25. 2x2 - 13x + 15 26. x2 - 6x + 13, R -31
27. 2x2 + 2x - 2, R 1 28. x2 + 3x - 7, R 15
29. 3x2 + 2x + 4, R -1 30. 41, 42, 43, 46; -2,
2i&quot;3, i&quot;3 31. 41, 42, 43, 44, 46, 412; -2, 2
2&quot;3, &quot;3 32. 18. 33. 24 34. 28 35. 20 36. 42
37. permutation; 720 38. combination; 792 39. combination;
20 40. x4 + 4x3y + 6x2y2 + 4xy3 + y4 41. -27x3
+ 108x2 - 144x + 64 42. 32r5 + 80r4q + 80r3q2
+ 40r2q3 + 10rq4 + q5 43. a3 + 12a2b + 48ab2
+ 64b3 44. about 0.29 or 29%
Chapter Test, Form B
1. 2x4 + 2x3 - 5; quartic trinomial 2. 10x2 - 4x;
quadratic binomial 3. 2x3 + 6x2 - 8x; cubic trinomial
4a. y = 0.000005208x3 - 0.00425x2 + 0.6204x + 54.57
4b. 79.78 years 5. -1.16, 1.45 6. 0.76, 2.96 7. -0.67
Algebra 2 Chapter 6
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(continued)
8. y = x3 - 7x2 + 14x - 8 9. y = x3 + 2x2 - 4x - 8
10. y = x4 + 23x2 - 50 11. 1, multiplicity 2; 2, multiplicity 3;
4 , multiplicity 4 12. - 3 ; -1, multiplicity 2; 0, multiplicity 2
3
2
13. -2, 0, 14. -3, 0, 2 15. -5, 3, 4 16. 2x2 + 10x + 20, R 51
17. x2 + 8x + 15 18. x2 - x - 1, R 6
19. 2x2 + 3x + 6, R 17 20. 41, 42, 43; 46; -6, -i, i
21. 41, 42, 44, 48, 416; 432; -4, 4,2&quot;2, &quot;2
22. -8 23. 120 24. 45 25. 70 26. 12
27. combination; 56 28. permutation; 720
29. x3 + 3x2y + 3xy2 + y3
30. 16x4 - 64x3 + 96x2 - 64x + 16
Alternative Assessment, Form C
; a, multiplicity 1,
b, multiplicity 1
y
0 Response is missing or inappropriate.
a. -1, -4 b. 1, -1
c. y = 12 (x - 2)(x + 1)(x + 4) and
y = (x - 4)(x - 1)(x + 1)
3 The roots are correct, and the functions are correctly
factored with the appropriate steps shown in using
division to solve for the roots.
2 The functions are factored correctly and most of the
1 Student unsuccessfully attempts to find the roots using
division, and has the functions mostly factored.
0 Response is missing or inappropriate.
x
O
a
errors. Multiplicities of the roots are not determined
correctly. Functions are not written in standard form
roots are found using division.
a.
1 Student’s graph of the polynomial contains significant
b
a. 350 b. 150 c. 210 d. 20
3 Student answers all four questions correctly.
2 Student answers three of the four questions correctly.
1 Student answers one or two of the four questions correctly.
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b.
; a, multiplicity 2,
b, multiplicity 1
y
0 Response is missing or inappropriate.
a
O b
x
a. r4 + 12r3s + 54r2s2 + 108rs3 + 81s4
b. Answers may vary. Sample: The concept of combinations, or nCr, can be used to find each of the coefficient
elements of Pascal’s Triangle. c. 47.8% d. 99.7%
3 Student writes a detailed explanation correlating
c. x2 - (a + b)x + ab = 0; x3 - (2a + b)x2 +
(a2 + 2ab)x - a2b = 0
d. 0,
2b 4 &quot;b2 2 4ac
2a
3 Student graphs the polynomial correctly and determines
the multiplicity of each root with no mistakes. Functions
are written in standard form correctly. Roots are found
for the equation with no errors.
2 Student graphs the polynomial correctly but does not
determine the multiplicities of the roots. Functions are
written in standard form correctly. Roots are found for
the equation with minor errors.
Pascal’s Triangle to the Binomial Theorem. Student
explains how the Binomial Theorem can be used to find
the elements of Pascal’s Triangle. Student also shows a
detailed method of using Pascal’s Triangle to expand the
binomial given. Student correctly determines the
probabilities.
2 Student provides most of the necessary information
relating the Binomial Theorem and Pascal’s Triangle.
Student correctly determines the expansion of the
binomial. Student correctly determines the probabilities.
1 Student attempts to describe the relationship between
the Binomial Theorem and Pascal’s Triangle. Student
correctly determines the probability of Katrina making
A’s in classes and making A’s in four of her seven
classes.
0 Response is missing or inappropriate.
Algebra 2 Chapter 6
43
(continued)
Cumulative Review
1. D 2. F 3. A 4. H 5. C 6. J 7. A 8. F
9. B 10. H 11. A 12. H 13. B
14. J 15. 5 columns 16a. 10 16b. 60
1
5 21 5
0
2
17. C
S 18. &pound; 7 21 5 &sect;
1 21
10 22 0
4
6
y
2
2
O
2
x
2
23. x3 - 3x2y2 + 3xy4 - y6 24. about 2.15 sec
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