Synthetic Division Polynomials Synthetic Division divide a polynomial

Synthetic Division Polynomials

Synthetic Division divide a polynomial by a polynomial To use synthetic division: • There must be a coefficient for every possible power of the variable. • The divisor must have a leading coefficient of 1.

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

Step #2: Write the constant r of the divisor x-r to the left and write down the coefficients. 5 0 -4 1 Since the divisor is x-3, r=3 6

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

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

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

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

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 45 123 372 15 41 124 378

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.

Step#3: Bring down the 1 st coefficient. Step#4: Multiply and add. Step#5: Repeat. -5 20 -1 4 1 -4 0 0 8 -2 10

Ex 8: Notice the leading coefficient of the divisor is 2 not 1. We must divide everything by 2 to change the coefficient to a 1.

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*Remember we cannot have complex fractions we must simplify.

Ex 9: 1 Coefficients