Synthetic Division Lesson For example : Suppose we were dividing x3 - 5x2 + 2x + 8 / x - 2. We can use synthetic division because the highest power of x in the divisor is 1 and the coefficient for x is 1. We must take the negation of the divisor. Since the first division will just be the coefficient in the dividend (since we know coefficient of divisor is 1) we will bring down that value and then start dividing with the negation of our second term. Note : We take negation of the -2 to start our division. Multiply the divisor 2 by the 1 we brought down (will always be 1) and bring the 2 up. Then combine and bring down the -3 Now multiply the -3 by the 2 and get -6, combine with the 2 and bring down the negative 4 Now multiply the -4 by the 2 and get -8, combine with the 2 and we get a remainder of 0 Our answer is 1x2 - 3x - 4 Suppose we are going to divide 2x2 - 3x + 4 / x + 5 -5| 2 -3 4 -10 65 2 -13 69 First we bring down coefficient of first number -> 2 Then multiply -5 x 2 and put -10 in next place - combine -3 and -10 and get -13 Then multiply -5 x -13 and put 65 in next place. Then combine 4 and 65 and bring down 69 So the answer is 2x - 13 r. 69