Homework
1
Lesson 6-1
pages 303–305 Exercises
12. –x4 + 3x3; quartic binomial
1. 10x + 5; linear binomial
13. y = x3 + 1
2. –3x + 5; linear binomial
14. y = 2x3 – 12
3. 2m2 + 7m – 3; quadratic binomial
15. y = 1.5x3 + x2 – 2x + 1
4. x4 – x3 + x; quartic trinomial
16. y = –3x3 – 10x2 + 100
5. 2p2 – p; quadratic binomial
17. a. males: y = –0.002571x2 +
0.2829x + 67.21
females: y = –0.002286x2 +
0.2514x + 74.82
b. males: y = 0.00008333x3 –
0.007571x2 + 0.3545x + 67.11
females: y = 0.00008333x3 –
0.007286x2 + 0.3231x + 74.72
c. The cubic model is a better fit.
6. 3a3 + 5a2 + 1; cubic trinomial
7. –x5; quintic monomial
8. 12x4 + 3; quartic binomial
9. 5x3; cubic monomial
10. –2x3; cubic monomial
11. 5x2 + 4x + 8; quadratic trinomial
2
Lesson 6-1
18. y = x3 – 2x2; 4335
28. 6x2; quadratic monomial
19. y = x3 – 10x2; 2023
29. x4 + 2x3; quartic binomial
20. y = –0.5x3 + 10x2; 433.5
30. 1 x5 + 2 x; quintic binomial
21. y = –0.03948x3 + 2.069x2 –
17.93x + 106.9; 206.07
31. a. V = 10 r 2
22. y = –0.007990x3 + 0.4297x2 –
6.009x + 43.57; 26.34
23. y = 0.01002x3 – 0.3841x2 +
5.002x + 2.132; 25.39
24. Check students’ work.
25. x3 + 4x; cubic binomial
26.
–4a4
+
a3
+
a2;
quartic trinomial
27. 7; constant monomial
2
3
b. V = 2
3
c. V = 2
3
r3
r 3 + 10 r 2
32. Answers may vary. Sample:
Cubic functions represent curvature
in the data. Because of their turning
points they can be unreliable for
extrapolation.
33. –c2 + 16; binomial
34. –9d3 – 13; binomial
3
Lesson 6-1
35. 16x2 – x – 5; trinomial
45. 6a2 + 3ab – 8; trinomial
36. 2x3 – 6x + 17; trinomial
46. 8x3 + 2x2; binomial
37. a + 4b; binomial
47. 30x3 – 10x2; binomial
38. –12y; monomial
48. 2a3 – 5a2 – 2a + 5;
polynomial of 4 terms
39. 8x2 – 6y; binomial
40. –3a + 2; binomial
41.
2x3
9x2
+
+ 5x + 27;
polynomial of 4 terms
42. –4x4 – 3x3 + 5x – 54;
polynomial of 4 terms
43. 80x3 – 109x2 + 7x – 75;
polynomial of 4 terms
44. 2x3 – 2x2 + 8x – 27;
polynomial of 4 terms
49. b3 – 6b2 + 9b; trinomial
50. x3 – 6x2 + 12x – 8;
polynomial of 4 terms
51. x4 + 2x2 + 1; trinomial
52. 8x3 + 60x2 + 150x + 126;
polynomial of 4 terms
53. a3 – a2b – b2a + b3;
polynomial of 4 terms
4
Lesson 6-1
54. a4 – 4a3 + 6a2 – 4a + 1;
polynomial of 5 terms
b.
55. 12s3 + 61s2 + 68s – 21;
polynomial of 4 terms
56. x3 + 2x2 – x – 2; trinomial
57. 8c3 – 26c + 12; trinomial
58. s4 – 2t 2s2 + t 4; trinomial
59. a. y = 0.7166x + 47.61
y = 0.0009365x3 – 0.0744x2 +
2.2929x + 41.4129
y = –0.00004789x4 + 0.004666x3 –
0.1647x2 + 2.9797x + 40.7831
The quartic model fits best.
c.
72.2 × 1015
5
Lesson 6-2
pages 311–313 Exercises 12. x(x – 9)(x + 2)
17. 2, –9
1. x2 + x – 6
13. 24.2, –1.4, 0, –5, 1
2. x3 + 12x2 + 47x + 60
14. 5.0, –16.9, 2, 6, 8
3. x3 – 7x2 + 15x – 9
15. a. h = x, = 16 – 2x,
w = 12 – 2x
18. 0, –5, 8
b. V = x(16 – 2x)(12 – 2x)
4. x3 + 4x2 + 4x
5. x3 + 10x2 + 25x
6. x3 – x
c.
7. x(x – 6)(x + 6)
8. 3x(3x – 1)(x + 1)
9. 5x(2x2 – 2x + 3)
194 in.3, 2.26 in.
19. –1, 2, 3
16. 1, –2
10. x(x + 5)(x + 2)
11. x(x + 4)2
6
Lesson 6-2
20. –1, 1, 2
30. 0, 1 (mult. 3)
31. –1, 0, 1
2
32. –1, 0, 1
21. y = x3 – 18x2 + 107x – 210
33. 4 (mult. 2)
22. y = x3 + x2 – 2x
34. 1, 2 (mult. 2)
23. y = x3 + 9x2 + 15x – 25
35. – 3, 1 (mult. 2)
24. y = x3 – 9x2 + 27x – 27
36. –1 (mult. 2), 1, 2
25. y = x3 + 2x2 – x – 2
37. 2 x3 blocks, 15 x2 blocks,
31 x blocks, 12 unit blocks
26. y = x3 + 6x2 + 11x + 6
27. y = x3 – 2x2
28. y = x3 –
7 2
x – 2x
2
29. –3 (mult. 3)
2
38. a. V = 2x3 + 15x2 + 31x + 12;
2x3 + 7x2 + 7x + 2
b. V = 8x2 + 24x + 10
39. V = 12x3 – 27x
7
Lesson 6-3
pages 318–320 Exercises
12. no
1. x – 8
13. x2 + 4x + 3
2. 3x – 5
14. x2 – 2x + 2
3. x2 + 4x + 3, R 5
15. x2 – 11x + 37, R –128
4. 2x2 + 5x + 2
16. x2 + 2x + 5
5. 3x2 – 7x + 2
17. x2 – x – 6
6. 9x – 12, R –32
18. –2x2 + 9x – 19, R 40
7. x – 10, R 40
19. x + 1, R 4
8. x2 + 4x + 3
20. 3x2 + 8x – 3
9. no
21. x2 – 3x + 9
10. yes
22. 6x – 2, R –4
11. yes
23. y = (x + 1)(x + 3)(x – 2)
8
Lesson 6-3
24. y = (x + 3)(x – 4)(x – 3)
25.
= x + 3 and h = x
26. 18
35. x – 1 is not a factor of x3 – x2 – 2x
because it does not divide into
x3 – x2 – 2x evenly.
27. 0
36. Answers may vary. Sample:
(x2 + x – 4) ÷ (x – 2)
28. 0
37. x2 + 4x + 5
29. 12
38. x3 – 3x2 + 12x – 35, R 109
30. 168
39. x4 – x3 + x2 – x + 1
31. 10
40. x + 4
32. 51
41. x3 – x2 + 1
33. 0
42. no
34. P(a) = 0; x – a is a factor of P(x).
43. yes
44. yes
9
Lesson 6-4
pages 324–326 Exercises
12. (x + 4)(x2 – 4x + 16)
1. –2, 1, 5
13. (x – 10)(x2 + 10x + 100)
2. –1, 0, 3
14. (5x – 3)(25x2 + 15x + 9)
3. 0, 1
15. 3, –3 ± 3i 3
4. 0, 8
16. –4, 2 ± 2i
5. 0, –1, –2
17. 5, –5 ± 5i 3
2
3
8. –0.5, 0, 3
2
18. –1, 1 ± i 3
2
19. 1 , –1 ± i 3
4
2
9. 1, 7
20. – 1 , 1 ± i 3
10. 4.8%
21. (x2 – 7)(x – 1)(x + 1)
11. about 5.78 ft × 6.78 ft × 1.78 ft
22. (x2 + 10)(x2 – 2)
6. 0, –3.5, 1
7. 0, –0.5, 1.5
2
4
10
Lesson 6-4
23. (x2 – 3)(x – 2)(x + 2)
35. –2, –3, 1, 2
24. (x – 2)(x + 2)(x – 1)(x + 1)
36. 1.71, 0.83
25. (x – 1)(x + 1)(x2 + 1)
37. 0, 1.54, 8.46
26. 2(2x2 – 1)(x + 1)(x – 1)
38. 0, 1.27, 4.73
27. ±3, ±1
39. –1.04, 0, 6.04
28. ±2
40. (n – 1)(n)(n + 1) = 210; 5, 6, 7
29. ±4, ±2i
41. about 3.58 cm, about 2.83 cm
30. ±3i, ±
31. ±
32. ±i
42. – 6 , 3 ± 3i 3
2
2, ±i
5, ±i
6
3
33. –1, 3.24, –1.24
34. –9, 0
5
43. 4 , –2 ± 2i
3
3
5
44. ±2
2, ±2i
45. ±5, ±i
3
2
2
11
Lesson 6-5
pages 333–334 Exercises
12. 1, –2, 1 ±
3
7
1. ±1, ±2; 1
13. –
2. ±1, ±2, ±3, ±6; 1, –2, –3
14. 4 +
6, –
3. ±1, ±2, ±4; –1
15. 1 +
10, 2 –
5,
13
3
2
4. ± 1 , ±1, ±2, ±4, ±8; no rational roots
16. 1 – i, 5i
5. ±1, ±2, ±4, ±8, ±16; –2
17. 2 – 3i, –6i
6. ±1, ±3, ±5, ±15; no rational roots
18. 4 + i, 3 – 7i
7. 2, ±i
5
19. x3 – x2 + 9x – 9 = 0
8. 5, ±i
7
20. x3 + 3x2 – 8x + 10 = 0
2
7
9. –3, 1, 2
10. –5, 1 ±
11. ± 1 , ±3
2
2
3
21. x3 – 2x2 + 16x – 32 = 0
22. x3 – 3x2 – 8x + 30 = 0
23. x3 – 6x2 + 4x – 24 = 0
12
Lesson 6-6
pages 337–338 Exercises
1. 3 complex roots;
number of real roots: 1 or 3
possible rational roots: ±1
5.
7 complex roots;
number of real roots: 1, 3, 5, or 7
possible rational roots: ±1, ±3
2. 2 complex roots;
number of real roots: 0 or 2
possible rational roots:
± 1 , ± 7 , ±1, ±7
6.
1 complex root;
number of real roots: 1
possible rational roots:
± 1 , ± 1 , ±1, ±2, ±4, ±8
3. 4 complex roots;
number of real roots: 0, 2, or 4
possible rational roots: 0
7.
3
3
4. 5 complex roots;
number of real roots: 1, 3, or 5
possible rational roots:
± 1 , ±1, ± 5 , ±5
2
2
8.
4
2
6 complex roots;
number of real roots: 0, 2, 4, or 6
possible rational roots:
± 1 , ±1, ± 7 , ±7
2
2
10 complex roots;
number of real roots: 0, 2, 4, 6, 8, or 10
possible rational roots: ±1
13
Lesson 6-6
9. –1, 1 ± i
4
18. 5 complex roots;
number of real roots: 1, 3, or 5
possible rational roots:
±1, ±2, ±3, ±6, ±9, ±18
7
10. 3, ±i
11. 4, 1 ± i
3
2
12. 2, ±
13. ±2, ±
19. 3 complex roots;
number of real roots: 1 or 3
possible rational roots:
± 1 , ± 2 , ±1, ± 4 , ±2, ±3, ±4, ±6, ±12
3
2
14. ±2, ±i
15. 0, 3 ± 3
16. –6, ±i
2
5
17. 4 complex roots;
number of real roots: 0, 2, or 4
possible rational roots:
± 1 , ±1, ±2, ± 13 , ±13, ±26
2
2
3
3
4
2
3
20. 6 complex roots;
number of real roots: 0, 2, 4, or 6
possible rational roots:
± 1 , ± 1 , ± 3 , ±1, ± 3 , ±2, ±3, ±4, ±6,
4
±8, ±12, ±24
2
21. 4, ±3i
22. –2, ±
5
14
Graphing Polynomial Functions
1.
2.
15
Graphing Polynomial Functions
3.
4.
16