Long Division of Polynomials Step by Step

Introduction to long division of polynomials:

In arithmetic, long division is the standard procedure suitable for dividing simple or complex multi digit numbers. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient.

(Source: Wikipedia)

Example Problems for Long Division of Polynomials Step by Step

Long division of polynomials step by step example problem 1:

Divide the given polynomial equation (4x⁵ + 12x⁴ + 29x² - 4x) by (x - 3) using long division method.

Solution:

Given polynomial equation is (4x⁵ + 12x⁴ + 29x² - 4x)

Dividend is (4x⁵ + 12x⁴ + 29x² - 4x) and divisor is (x - 3)

                         ______________________
             (x - 3) ) 4x⁵ + 12x⁴ + 29x² - 4x      ( (4x⁴ + 24x³ + 72x² + 245x + 731)
                         4x⁵ - 12x⁴      ( - )
   ______________________
24x⁴ + 29x² - 4x
    24x⁴ - 72x³ ( - )

   ______________________
   72x³ + 29x² - 4x
   72x³ - 216x²    ( - )
   _______________________
245x² - 4x
                                            245x² - 735x ( - )
                         ________________________
                                             731x
                                             731x - 2193 ( - )
   _______________________
                                                       2193

Quotient = 4x⁴ + 24x³ + 72x² + 245x + 731 and remainder value is 2193

Answer:

The final answer is Quotient = 4x⁴ + 24x³ + 72x² + 245x + 731 and remainder value is 2193

Long division of polynomials step by step example problem 2:

Divide the given polynomial equation (x² - 52x + 10) by (x + 1) using long division method.

Solution:

Given polynomial equation is (x² - 52x + 10)

Dividend is (x² - 52x + 10) and divisor is (x + 1)

                         ______________________
             (x + 1) ) x² - 52x + 10               ( (x - 53)
                         x² + x      ( - )
   ______________________
- 53x + 10
- 53x - 53 ( - )

______________________
63

Quotient = x - 53 and remainder value is 63

Answer:

The final answer is Quotient = x - 53 and remainder value is 63

Long division of polynomials step by step example problem 3:

Divide the given polynomial equation (9x³ - 32x² - 4x) by (x - 2) using long division method.

Solution:

Given polynomial equation is (9x³ - 32x² - 4x)

Dividend is (9x³ - 32x² - 4x) and divisor is (x - 2)

                         ______________________
          (x - 2) ) 9x³ - 32x² - 4x       ( (9x² - 14x - 32)
                         9x³ - 18x²      ( - )
   ______________________
- 14x² - 4x
- 14x² + 28x    ( - )

   ______________________
   - 32x
   - 32x + 64 ( - )
   _______________________
   - 64

Quotient = 9x² - 14x - 32 and remainder value is - 64

Answer:

The final answer is Quotient = 9x² - 14x - 32 and remainder value is - 64

Practice Problems for Long Division of Polynomials Step by Step

Polynomial division remainder practice problem 1:
Divide the given polynomial equation (21x² + 53x + 70) by (x + 1) using long division method.
Answer:
The final answer is quotient = 21x + 32 and the remainder is 38
Polynomial division remainder practice problem 2:
Divide the given polynomial equation (10x⁴ + 43x + 9) by (x - 4) using long division method.
Answer:
The final answer is quotient = 10x³ + 40x² + 160x + 683 and the remainder is 2741

More books about long division for kids

Mathimagination Series: Book A, beginning multiplication and division; Book B, operations with whole numbers; Book C, number theory, sets and number bases; Book D, fractions; Book E, decimals and percent

Decimals and Percentages With Pre- And Post-Tests: Place Value, Addition, Subtraction, Multiplication, Division

Read more