DIVIDING A POLYNOMIAL BY A BINOMIAL

Divide. Write your answer in fraction form.

Problem 1 :

(2x⁵ – 15x³ – 9x² + 11x + 12) ÷ (x + 2)

Solution :

Quotient = 2x⁴ – 4x³ – 7x² + 5x + 1

Remainder = 10

Fraction form :

Problem 2 :

(x⁴ – x³ – 19x² - 3x - 19) ÷ (x - 5)

Solution :

Quotient = x³ + 4x² + x + 2

Remainder = -9

Fraction form :

Problem 3 :

(10x⁴ – 4x³ + 14x² - 14x - 16) ÷ (2x - 2)

Solution :

(10x⁴ – 4x³ + 14x² - 14x - 16) ÷ (2x - 2)

2(5x⁴ – 2x³ + 7x² – 7x – 8) ÷ 2(x – 1)

(5x⁴ – 2x³ + 7x² – 7x – 8) ÷ (x – 1)

Quotient = 5x³ + 3x² + 10x + 3

Remainder = -5

Fraction form :

Problem 4 :

(9x⁵ – 9x⁴ – x³ - 12x² + x - 11) ÷ (3x - 5)

Solution :

Quotient = 3x⁴ + 2x³ + 3x² + x + 2

Remainder = -1

Fraction form :

Problem 5 :

(16x⁴ + 4x³ + 2x² - 21x + 7) ÷ (4x - 1)

Solution :

Quotient = 4x³ + 2x² + x - 5

Remainder = 2

Fraction form :

Problem 6 :

(6x⁵ + 21x⁴ – 14x³ - 8x² + x - 6) ÷ (x + 4)

Solution :

Quotient = 6x⁴ - 3x³ - 2x² + 0x + 1

Remainder = -10

Fraction form :