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



 
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