A-18 Answers to Selected Exercises 11. (a) 4. (a) Positive Negative Nonreal Complex 3 1 0 1 1 2 Positive Negative Nonreal Complex 4 0 0 2 0 2 0 0 4 Positive Negative Nonreal Complex 2 1 0 0 1 2 Summary Exercises on Polynomial Functions, Zeros, and Graphs 1. (a) Positive Negative Nonreal Complex 2 1 0 0 1 2 (b) {1, {2, {3, {4, {6, {8, {12, {24, { 1 2 , { 3 2 , { 1 3 , { 2 3 , { 4 3 , { 8 3 , { 1 6 (c) - 1 2 , 4 3 , 6 (d) no other complex zeros 2. (a) (b) {1, {3, { 1 2 , { 3 2 (c) -1, 1 2 , 3 (d) no other complex zeros 3. (a) (b) {1, {2, {4, {8, { 1 3 , { 2 3 , { 4 3 , { 8 3 (c) 2 3 , 1 (d) -2i, 2i (b) {1, {2, {3, {6, {9, {18, { 1 2 , { 3 2 , { 9 2 (c) - 1 2 , 2 (d) -3i, 3i Positive Negative Nonreal Complex 3 2 0 3 0 2 1 2 2 1 0 4 Positive Negative Nonreal Complex 1 3 0 1 1 2 Positive Negative Nonreal Complex 1 3 0 1 1 2 Positive Negative Nonreal Complex 4 0 0 2 0 2 0 0 4 Positive Negative Nonreal Complex 2 2 0 2 0 2 0 2 2 0 0 4 Positive Negative Nonreal Complex 1 3 0 1 1 2 (b) {1, {2, { 1 2 , { 1 3 , { 2 3 , { 1 6 (c) 1 3 , 1 2 (d) -22, 22 6. (a) (b) {1, {2, {3, {4, {6, {12, { 1 5 , { 2 5 , { 3 5 , { 4 5 , { 6 5 , { 12 5 (c) -2 , 2 5 (d) - 23, 23 7. (a) (b) 0, {1, {2, {4, {8, {16 (c) 0, 2 (multiplicity 2) (d) 1 - i23, 1 + i23 8. (a) 8. (b) {1, {3, {9, { 1 2 , { 3 2 , { 9 2 (c) -3 (multiplicity 2) (d) 2 - 26 2 , 2 + 26 2 9. (a) (b) {1, { 1 2 , { 1 4 , { 1 8 (c) -1, 1 2 (d) - 1 4 - 23 4 i, - 1 4 + 23 4 i 10. (a) (b) {1, {2, {3, {6, { 1 2 , { 3 2 (c) -3, -2, 1 2 , 1 (multiplicity 2) (d) no other complex zeros (b) {1, {2, {3, {6 (c) -3, -1 (multiplicity 2), 2 (d) no other real zeros (e) no other complex zeros (f) 1-3, 02, 1-1, 02, 12, 02 (g) 10, -62 (h) ƒ142 = 350; 14, 3502 (i) Positive Negative Nonreal Complex 3 1 0 1 1 2 5. (a) x y 400 –200 2 0 f(x) = –2x5 + 5x4 + 34x3 – 30x2 – 84x + 45 Positive Negative Nonreal Complex 3 2 0 3 0 2 1 2 2 1 0 4 (j) x y 2 0 –3 –6 –20 f(x) = x4 + 3x3 – 3x2 – 11x – 6 12. (a) (b) {1, {3, {5, {9, {15, {45, { 1 2 , { 3 2 , { 5 2 , { 9 2 , { 15 2 , { 45 2 (c) -3, 1 2 , 5 (d) - 23, 23 (e) no other complex zeros (f) 1-3, 02, A1 2 , 0B , 15, 02, A -23, 0B , A 23, 0B (g) 10, 452 (h) ƒ142 = 637; 14, 6372 (i) (j)
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