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 x 2 + 5x + 6 by x + 2.      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 x 2 + 5x + 6 are (x+2) and (x+3)  h/w: p. 324: 13, 14, 16, 17

Divide (x 3 + 2x 2 - 5x – 6) by (x+1)