# DIVIDING POLYNOMIALS USING SYNTHETIC DIVISION WORKSHEET

Use synthetic division to divide the polynomials given below, then find the quotient and remainder.

Problem 1 :

(x² + 8x + 1) ÷ (x - 4)

Solution

Problem 2 :

(4x² - 13x - 5) ÷ (x - 2)

Solution

Problem 3 :

(2x² - x + 7) ÷ (x + 5)

Solution

Problem 4 :

(x³ - 4x + 6) ÷ (x + 3)

Solution

Problem 5 :

(x² + 9) ÷ (x - 3)

Solution

Problem 6 :

(3x³ - 5x² - 2) ÷ (x - 1)

Solution

Problem 7 :

(x4 – 5x³ - 8x² + 13x - 12) ÷ (x - 6)

Solution

Problem 8 :

(x4 + 4x³ + 16x - 35) ÷ (x + 5)

Solution

1)  quotient is x + 12 and remainder is 49.

2)  quotient is 4x - 5 and remainder is -5

3)  quotient is 2x - 11 and remainder is 62.

4)  quotient is x² - 3x + 5 and remainder is -9

5)  quotient is x + 3 and remainder is 18

6) quotient is 3x² - 2x - 2 and remainder is -4

7)  quotient is x³ + x² - 2x + 1 and remainder is -6

8)  quotient is x³ - x² + 5x - 9 and remainder is 10.

Use synthetic division to evaluate the function for the indicated value of x.

Problem 1 :

f(x) = -x² - 8x + 30; x = -1

Solution

Problem 2 :

f(x) = 3x² + 2x – 20; x = 3

Solution

Problem 3 :

f(x) = x³ - 2x² + 4x + 3; x = 2

Solution

Problem 4 :

f(x) = x³ + x² - 3x + 9; x = -4

Solution

Problem 5 :

f(x) = x³ - 6x + 1; x = 6

Solution

Problem 6 :

f(x) = x³ - 9x – 7; x = 10

Solution

Problem 7 :

f(x) = x4 + 6x² - 7x + 1; x = 3

Solution

Problem 8 :

f(x) = -x4 - x³ - 2; x = 5

Solution

1)  f(-1) = 37

2)  f(3) = 13

3)  f(2) = 11

4) f(-4) = -27

5)  f(6) = 181

6)  f(10) = 903

7)  f(3) = 115

8)  f(5) = -152

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