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6-3 DIVIDING POLYNOMIALS Synthetic division Using synthetic division to perform long division of polynomials Procedures to follow for synthetic division: 1. First, write down all the coefficients, and put the opposite number of the divisor at the left of the vertical line 2. Bring down the first number below the horizontal line 3. Multiply the number at the left by the number you brought down and put the answer above the line and directly under the second number. 4. Add the two numbers and put the answer under the line 5. Repeat steps 3 and 4 until the last term has been used Example: Divide x2 + 5x + 6 by x + 2. -2 1 5 6 write down all the coefficients, and put the zero from x+2 = 0 (x = -2) at the left Bring down the first number (1) Multiply (-2) by (1) and put the answer under the (5) Add 5 + (-2) and put the answer under the line Multiply (-2) by (3) and put the answer under the (6) Add (-6) to the (6) and the put the answer under the line If the last number is “0” that means the answer is a factor of the expression Rewrite the answer as a polynomial beginning with one exponent less than the highest exponent of the original polynomial (x+3) So the factors of x2 + 5x + 6 are (x+2) and (x+3) h/w: p. 324: 13, 14, 16, 17 Divide (x3 + 2x2 - 5x – 6) by (x+1)