Assignment 4 Solutions

# Assignment 4 Solutions - 1-4 ↓ 1 2-1 4 1 2-1 4-4 3 x 4 2...

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Problem Set 1. Divide using long division: x 4 + 2 x 3 + 2 x 2 - 10 x - 20 by x - 2. x - 2 x 3 +4 x 2 +10 x +10 x 4 +2 x 3 +2 x 2 - 10 x - 20 x 4 - 2 x 3 4 x 3 +2 x 2 4 x 3 - 8 x 2 10 x 2 - 10 x 10 x 2 - 20 x 10 x - 20 10 x - 20 0 x 3 + 4 x 2 + 10 x - 30 remainder 0. 2. Divide using long division: 3 x 4 + 2 x 3 - x 2 + 4 x - 5 by x - 1. x - 1 3 x 3 +5 x 2 +4 x +8 3 x 4 +2 x 3 - x 2 +4 x - 5 3 x 4 - 3 x 3 5 x 3 - x 2 5 x 3 - 5 x 2 4 x 2 +4 x 4 x 2 - 4 x 8 x - 5 8 x - 8 3 x 3 + 5 x 2 + 4 x - 8 remainder 3. 3. Divide using long division: - x 4 - 4 x 3 + 14 x 2 + 2 x - 1 by x 2 - 2 x + 1. x 2 - 2 x + 1 - x 2 - 6 x +3 - x 4 - 4 x 3 +14 x 2 +2 x - 1 - x 4 +2 x 3 - x 2 - 6 x 3 +15 x 2 +2 x - 6 x 3 +12 x 2 - 6 x 3 x 2 +8 x - 1 3 x 2 - 6 x +3 14 x - 4

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- x 2 - 6 x + 3 remainder 14 x - 2. 4. Divide using long division: - x 5 + x 4 - 2 x 3 + 2 x 2 + 4 x + 1 by x 3 - 2 x + 2. x 3 + 0 x 2 - 2 x + 2 - x 2 + x - 4 - x 5 + x 4 - 2 x 3 +2 x 2 +4 x +1 - x 5 +0 x 4 +2 x 3 - 2 x 2 x 4 - 4 x 3 +4 x 2 +4 x x 4 +0 x 3 - 2 x 2 +2 x - 4 x 3 +6 x 2 +2 x +1 - 4 x 3 +0 x 2 +8 x - 8 6 x 2 - 6 x +9 - x 2 + x - 4 remainder 6 x 2 - 6 x + 9. 5. Divide using Synthetic division: x 6 - 4 x 5 - 7 x 4 - 3 x 3 - 2 x 2 + 6 x + 9 by x - 1. 1 1 - 4 - 7 - 3 - 2 6 9 1 - 3 - 10 - 13 - 15 9 1 - 3 - 10 - 13 - 15 - 9 0 x 5 - 3 x 4 - 10 x 3 - 13 x 2 - 15 x - 9 remainder 0. 6. Divide using Synthetic division: 4 x 6 + x 5 - x 4 + 3 x 3 + 5 x 2 + 3 x + 10 by x + 1. - 1 4 1 - 1 3 5 3 10 ↓ - 4 3 - 2 - 1 - 4 1 4 - 3 2 1 4 - 1 11 4 x 5 - 3 x 4 + 2 x 3 + x 2 + 4 x - 1 remainder 11. 7. Divide using Synthetic division: x 6 + x 5 + x 4 + x 3 + x 2 + x - 1 by x 2 + x - 1. - 1 1 1 1 1 1 1 1 - 1 ↓ - 1 0 - 2
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Unformatted text preview: 1-4 ↓ 1 2-1 4 1 2-1 4-4 3 x 4 + 2 x 2-x + 4 remainder-4 x + 3. 8. Divide using Synthetic division: 4 x 6 + x 5-x 4 + 3 x 3 + 5 x 2 + 3 x + 10 by x 3 + x 2 + x + 1.-1-1-1 4 1-1 3 5 3 10 ↓ -4 3 2-4 ↓-4 3 2-4 ↓-4 3 2-4 4-3-2 4 6 1 6 4 x 3-3 x 2-2 x + 4 remainder 6 x 2 + x + 6. 9. (2 points) Find a maximum and minimum (try small integers from 0 to 10 and 0 to-10) for the roots of: x 4 + 3 x 3 + 2 x 2 + 4 x-17. For this question I found 2 and -4. These are the smallest integers that work.-4 1 3 2 4-17 ↓ -4 4-24 80 1-1 6-20 63 2 1 3 2 4-17 ↓ 2 10 24 56 1 5 12 28 39...
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Assignment 4 Solutions - 1-4 ↓ 1 2-1 4 1 2-1 4-4 3 x 4 2...

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