Dividing Polynomials: Synthetic Division

Essential Question How do I use synthetic division to determine if something is a factor of a polynomial?

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Synthetic Division - To use synthetic division: divide a polynomial by a linear binomial To use synthetic division: There must be a coefficient for every possible power of the variable. The divisor must be a linear binomial with a leading coefficient of 1. Ex: (x – a) or (x + a)

Step #1: Write the terms of the. polynomial so the degrees are in Step #1: Write the terms of the polynomial so the degrees are in descending order. Since the numerator does not contain all the powers of x, you must include a 0 for the

5 -4 1 6 Since the divisor is x-3, r=3 Step #2: Write the constant r of the divisor x-r to the left and write down the coefficients. 5 -4 1 6 Since the divisor is x-3, r=3

Step #3: Bring down the first coefficient, 5.

15 15 5 Step #4: Multiply the first coefficient by r, so and place under the second coefficient then add. 5 15 15

Step #5: Repeat process multiplying. the sum, 15, by r; Step #5: Repeat process multiplying the sum, 15, by r; and place this number under the next coefficient, then add. 5 15 45 41

Step #5 cont.: Repeat the same procedure. Where did 123 and 372 come from? 5 15 45 41 123 372 124 378

Step #6: 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. 5 15 45 41 123 124 372 378

The quotient is: Remember to place the remainder over the divisor.

Ex 7: Step#1: Powers are all accounted for and in descending order. Step#2: Identify r in the divisor. Since the divisor is x+4, r=-4 .

4 -4 20 8 -5 -1 1 -2 10 Step#3: Bring down the 1st coefficient. Step#4: Multiply and add. Step#5: Repeat. 4 -4 20 8 -5 -1 1 -2 10

Assignment Complete the worksheet.