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Mastering Synthetic Division: Techniques and Examples

Learn the fundamentals of synthetic division, including step-by-step instructions, important notes, and practical examples to enhance your understanding.

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Mastering Synthetic Division: Techniques and Examples

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  1. Section 3.3 – Polynomials and Synthetic Division

  2. 3x 3x x

  3. 3 1 1 2 1 -4 2 -5 -3 -3 3 -1 -8 -1 2 -1 2 -3 1 3 2 3 0 1

  4. 3 5 4 2 4 -3 -8 4 27 57 12 19 61 9 2 -5 -28 14 25 -15 10 -3 -1 5

  5. 2 3 16 1 16 -32 -81 162 -162 32 0 0 0 -81 1 -2 -1 1 3 6 3 2 7 1

  6. 3 4 1 1 1 0 -5 2 12 3 9 14 3 4 1 0 -17 0 16 -16 16 -4 4 -1 -4 4 0

  7. 2/3 2 6 3 -1/2 2 6 -4 3 -2 2 4 0 0 0 3 2 5 4 5 2 -2 -2 -1 -1 4 4 2 0

  8. 1/4 4 4 4 -1 -4 1 -1 1 0 0 0 -4

  9. 4 -1/2 2 4 0 -13 -6 1 6 -2 0 -2 -12

  10. 3 1 1 0 -5 2 12 3 9 14 3 4

  11. 4 1 1 0 -17 0 16 -16 16 -4 4 -1 -4 4 0

  12. Synthetic Division Summary • Set denominator = 0 and solve (box number) • Bring down first number • Multiply by box number and add until finished • Remainder goes over divisor Notes of Caution • ALL terms must be represented (even if coefficient is 0) • If box number is a fraction, must divide final answer by • the denominator • To evaluate a function at a particular value, you may EITHER: • Substitute the value and simplify OR • Complete synthetic division…the remainder is your answer

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