1. Table of Contents Polynomials: Synthetic Division If a polynomial is divided by a linear factor of the form x – c, then a process know as synthetic division can be used in place of "long division". Example: Synthetically divide: (x 3 + 4x 2 – 5)  (x + 2). First, write the coefficients of the terms in the dividend, (1x 3 + 4x 2 + 0x – 5) beginning with the coefficient of the highest degree term and descending through all the terms to the constant term. 1 4 0- 5

2. Table of Contents Polynomials: Synthetic Division Slide 2 140 - 5 - 2 Next, write the value of c in the position shown along with the line segments. Note, the divisor is (x + 2). Compare with x – c to see that c is - 2. Next, write the first entry in the dividend row as shown. 1 Next, multiply this value by c and place the result in the next column as shown. multiply - 2 Add the column figures as shown. + 2 Repeat this process of multiplying and adding as shown - 4 + + 3 8

3. Table of Contents Polynomials: Synthetic Division Slide 3 140 - 5 - 2 1 2 - 4 3 8- 2 Last, write the quotient polynomial and remainder by interpreting the row of numbers below the line as shown. REM 1x 2 + 2x – 4 QUOTIENT Note the degree of the quotient is one less than the degree of the divisor. Try: Synthetically divide: (2x 3 – 30x + 1)  (x – 4). The quotient is 2x 2 + 8x + 2 and the remainder is 9.

4. Table of Contents Polynomials: Synthetic Division