Lesson 4

# Lesson 4 - 6-x 5 2 x 4 3 x 3 x 2-4 x-17 by x 3-2 x 2 3 x-3...

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Problem Set 1. Divide using long division: x 4 +5 x 3 +3 x 2 - 2 x - 1 by x +1. ( x 3 +4 x 2 - x - 1) 2. Divide using long division: 2 x 4 + 3 x 3 - 7 x 2 + 4 x - 1 by x - 1. (2 x 3 + 5 x 2 - 2 x + 2 remainder 1) 3. Divide using long division: - 2 x 4 + 5 x 3 - 12 x 2 + 2 x + 1 by x 2 - 3 x + 5. ( - 2 x 2 - x - 10 remainder - 8 x + 26) 4. Divide using long division: - x 5 + x 4 - 2 x 3 - 3 x 2 + 4 x + 1 by x 3 - x + 2. ( - x 2 - 3 remainder x + 7) 5. Divide using Synthetic division: x 6 + 3 x 5 + 6 x 4 - 3 x 3 - 4 x 2 + 2 x - 1 by x + 1. ( x 5 + 2 x 4 + 4 x 3 - 7 x 2 + 3 x - 1) 6. Divide using Synthetic division: 7 x 6 - 2 x 5 + 4 x 4 - 9 x 3 - x 2 + 2 x + 1 by x - 1. (7 x 5 + 5 x 4 + 9 x 3 - x + 1 remainder 2) 7. Divide using Synthetic division: x 6 + x 5 + x 4 + x 3 + x 2 + x - 1 by x 2 + x - 1. ( x 4 + 2 x 2 - x + 4 remainder -4x+3) 8. Divide using Synthetic division: x
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Unformatted text preview: 6-x 5 + 2 x 4 + 3 x 3 + x 2-4 x-17 by x 3-2 x 2 + 3 x-3. ( x 3 + x 2 + x + 5 remainder 11 x 2-16 x-2) 9. Find a maximum for the roots of: x 4-3 x 3 + x 2 + 4 x-17 Here 3 would work as a maximum, -2 would work as a minimum. Why is that? When you divide by x-a and get all positive coeﬃcitents (all negative) then a is higher or equal to all your roots. When you divide by x-a and get alternating coeﬃcients then a is smaller or equal to all your roots....
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