Synthetic Division of Polynomials

1. Synthetic Division of Polynomials Be able to use synthetic division to divide polynomials.

2. Synthetic Division • There is another way to divide polynomials called synthetic division. • This method can only be used when the divisor (the polynomial that you are dividing by) is in the form (x – a), where a is a number. • If the coefficient of x in the divisor is any number other than 1, you cannot use synthetic division. Polynomials

3. Example Divide • The divisor is , so a is3. • Write a in the upper right corner and then write the coefficientsof thedividend. • Draw a horizontal line and the bring down the first coefficient. 3 2 -1 -10 2 -10 -1 2 3 Polynomials

4. Example (cont.) 3 2 -1 -10 • Multiply the 2 by the 3 and put the product in the second column. • Add the numbers in the column. • Multiply the sum by the 3 and put the product in the third column. • Add the numbers in the column. Draw a box around the last number. 6 15 2 5 5 Polynomials

5. Example (cont.) 3 2 -1 -10 • The numbers on the bottom row are the coefficients of the quotient (the answer), and the last number is the remainder. • So the quotient of the example is: 6 15 2 5 5 Polynomials

6. Examples to Try • . Hint: a = – 2 We write the quotient this way: 7 10 – 2 4 2 – 8 4 12 – 1 Polynomials

7. Examples to Try a = 5 We write the quotient this way: 2 5 – 12 – 6 10 20 4 2 8 Polynomials