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Polynomial long division tutorial

Polynomial long division is simple.

The following example will help you to divide a polynomial by a polynomial.

We will explain how to do a long division problem with polynomials step by step.

Polynomial long division example

Simple problem.

We will divide the polynomial (a2 - 9a - 22) by the polynomial (a - 11):

(a2 - 9a - 22)/(a - 11)

The (a2 - 9a - 22) is a dividend and the (a - 11) is a divisor.

We use the long division symbol:

                   
a - 11)a2 - 9a - 22

Step 1.

Divide the first term of the dividend (the a2) by the first term of the divisor (the a):

a2/a = a

Put the result (a) over the long division symbol:

      a            
a - 11)a2 - 9a - 22

Step 2.

Multiply the (a) through the divisor a - 11:

a(a - 11) = a2 - 11a

Step 3.

Subtract the (a2 - 11a) from the two leading terms of the dividend:

      a            
a - 11)a2 - 9a - 22
     -(a2 - 11a)
             2a

Step 4.

Carry down the last dividend term:

      a            
a - 11)a2 - 9a - 22
     -(a2 - 11a)
            2a - 22

Step 5.

Divide the first term of the 2a - 22 (the 2a) by the first term of the divisor (the a):

2a/a = 2

Put the result 2 over the long division symbol:

      a + 2        
a - 11)a2 - 9a - 22
     -(a2 - 11a)
            2a - 22

Step 6.

Multiply the 2 through the divisor a - 11:

2(a - 11) = 2a - 22

Step 7.

Subtract the 2a - 22 from the 2a - 22:

      a + 2        
a - 11)a2 - 9a - 22
     -(a2 - 11a)
            2a - 22
          -(2a - 22)
               0

The final result of the division:

(a2 - 9a - 22)/(a - 11) = a + 2

The problem is solved.