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

• How to do long division step by step?
• How to do long division with remainders?
• How do you do long division with decimals?
• Understanding long division as repeated subtraction
• Teaching Long Division
• Double Division with 3 Digit Divisors
• How to do long division with two digit quotients?
• Long Division of Polynomials Step by Step
• How to do long division with 2 digit divisor?
• How to do long division with two digit quotients?