DIVIDING POLYNOMIALS USING SYNTHETIC DIVISION

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

Problem 1 :

(x² + 8x + 1) ÷ (x - 4)

Solution :

Arrange dividend and the divisor in standard form.

Then,

x² + 8x + 1 (standard form of dividend)

x - 4 (standard form of divisor)

Find out the zero of the divisor.

x - 4 = 0

x = 4

Therefore, the quotient is x + 12

And the remainder is 49.

Problem 2 :

(4x² - 13x - 5) ÷ (x - 2)

Solution :

Find out the zero of the divisor.

x - 2 = 0

x = 2

Therefore, the quotient is 4x - 5

And the remainder is -5

Problem 3 :

(2x² - x + 7) ÷ (x + 5)

Solution :

Find out the zero of the divisor.

x + 5 = 0

x = - 5

Therefore, the quotient is 2x - 11

And the remainder is 62.

Problem 4 :

(x³ - 4x + 6) ÷ (x + 3)

Solution :

Find out the zero of the divisor.

x + 3 = 0

x = -3

Therefore, the quotient is x² - 3x + 5

And the remainder is -9

Problem 5 :

(x² + 9) ÷ (x - 3)

Solution :

Find out the zero of the divisor.

x – 3 = 0

x = 3

Therefore, the quotient is x + 3

And the remainder is 18

Problem 6 :

(3x³ - 5x² - 2) ÷ (x - 1)

Solution :

Find out the zero of the divisor.

x - 1 = 0

x = 1

Therefore, the quotient is 3x² - 2x - 2

And the remainder is -4

Problem 7 :

(x⁴ – 5x³ - 8x² + 13x - 12) ÷ (x - 6)

Solution:

Find out the zero of the divisor.

x – 6 = 0

x = 6

Therefore, the quotient is x³ + x² - 2x + 1

And the remainder is -6

Problem 8 :

(x⁴ + 4x³ + 16x - 35) ÷ (x + 5)

Solution :

Find out the zero of the divisor.

x + 5 = 0

x = -5

Therefore, the quotient is x³ - x² + 5x - 9

And the remainder is 10.