DIVIDING A POLYNOMIAL BY A BINOMIAL

Divide the given polynomial using long division. Write your answer in fraction form.

Problem 1 :

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

Solution

Problem 2 :

(x⁴ – x³ – 19x² - 3x - 19) ÷ (x - 5)

Solution

Problem 3 :

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

Solution

Problem 4 :

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

Solution

Problem 5 :

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

Solution

Problem 6 :

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

Solution

Answer Key

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

Problem 1 :

Without performing division, find the remainder when

x³ + 2x² - 7x + 5 is divided by x - 1

Solution

Problem 2 :

Without performing division, find the remainder when

x⁴ - 2x² + 3x - 1 is divided by x + 2

Solution

Problem 3 :

Find a given that:

when x³ - 2x + a is divided by x - 2, the remainder is 7.

Solution

Problem 4 :

Find a given that:

when 2x³ + x² + ax - 5 is divided by x + 1, the remainder is -8

Solution

Problem 5 :

Find a and b given that when x³ + 2x² + ax + b is divided by x - 1 the remainder is 4, and when divided by x + 2 the remainder is 16.

Solution

Problem 6 :

2xⁿ + ax² - 6 leaves a remainder of -7 when divided by x - 1, and 129 when divided by x + 3. Find a and n given that n∈Z⁺.

Solution

Problem 7 :

When P(z) is divided by z² - 3z + 2 the remainder is 4z - 7. Find the remainder when P(z) is divided by:

a. z - 1    b. z - 2

Solution

Problem 8 : 

When P(z) is divided by z + 1 the remainder is -8 and when divided by z - 3 the remainder is 4. Find the remainder when P(z) is divided by (z - 3) (z + 1).

Solution