# Lets look at how to do this using Lets look at how to do this using the example: 5x #1 4 4 x x 6 ( x 3) 2 In order to use synthetic division these two things must happen: #2 The divisor must There must be a coefficient for have a leading every possible

coefficient of 1. power of the variable. Step #1: Write the terms of the polynomial so the degrees are in descending order. 4 3 2 5x 0x 4x x 6 Since the numerator does not contain all the powers of x, you must include a 0 for the x 3 . Step #2: Write the constant a of the divisor

x- a to the left and write down the coefficients. Since the divisor x 3, then a 3 5x 3 4 0x 3 4x 2

x 6 5 0 4

1 6 Step #3: Bring down the first coefficient, 5. 3 5 0 4 1 6 5 Step #4: Multiply the first coefficient by r (3*5). 3 5

0 15 5 4 1 6 Step #5: After multiplying in the diagonals, add the column. Add the column 3 5 0

15 5 15 4 1 6 Step #6: Multiply the sum, 15, by r; 153=15, and place this number under the next coefficient, then add the column again. 3 Add 5 0 4 1 6

15 45 5 15 41 Multiply the diagonals, add the columns. Step #7: Repeat the same procedure as step #6. 3 5 Add Columns 0 Add Columns

4 1 Add Columns Add Columns 6 15 45 123 372 5 15 41 124 378 Step #8: Write the quotient. The numbers along the bottom are

coefficients of the power of x in descending order, starting with the power that is one less than that of the dividend. The quotient is: 378 5x 15x 41x 124 x 3 3 2 Remember to place the remainder over the divisor. Try this one:

1) ( t 3 6t 2 1) (t 2) 2 1 6 0 1 2 16 32 1 8 16 31 31 Quotient 1t 8t 16 t 2 2