Section 3.3 – Polynomials and Synthetic Division

3x 3x x

3 1 -4 2 -5 1 3 -3 -3 -1 -1 -8 1 2 -1 2 -3 2 2 1 3 1 3

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

2 16 -32 -81 162 16 32 -162 -81 3 1 -2 -1 1 1 3 3 6 1 2 7

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

2/3 6 -4 3 -2 6 4 2 3 3 -1/2 2 5 4 5 2 2 -1 -2 -1 -2 4 2 4 2

1/4 4 -1 -4 1 4 1 -1 -4 4

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

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

4 1 0 -17 0 16 1 4 16 -4 -16 4 -1 -4

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