SBP-Program

f

tw

in

How to divide polynomials with two variables

Dividing polynomials with two variables is simple.

The following example will help you to divide polynomials with two variables.

We will explain how to divide polynomials with two variables step by step.

Dividing polynomials with two variables

Simple example.

We will divide the polynomial with two variables (3a2b2 - 4ab - 4) by the polynomial (ab - 2):

(3a2b2 - 4ab - 4)/(ab - 2)

The (3a2b2 - 4ab - 4) is a dividend and the (ab - 2) is a divisor.

We use the long division symbol:

                      
ab - 2)3a2b2 - 4ab - 4

To begin let's divide the first term of the dividend (the 3a2b2) by the first term of the divisor (the ab):

3a2b2/ab = 3ab

Put the result 3ab over the long division symbol:

      3ab             
ab - 2)3a2b2 - 4ab - 4

Multiply the 3ab through the divisor (ab - 2):

3ab(ab - 2) = 3a2b2 - 6ab

Subtract the 3a2b2 - 6ab from the two leading terms of the dividend:

      3ab             
ab - 2)3a2b2 - 4ab - 4
     -(3a2b2 - 6ab)
               2ab

Carry down the last dividend term (the 4):

      3ab             
ab - 2)3a2b2 - 4ab - 4
     -(3a2b2 - 6ab)
               2ab - 4

Divide the first term of the 2ab - 4 (the 2ab) by the first term of the divisor (the ab):

2ab/ab = 2

Put the result 2 over the long division symbol:

      3ab + 2         
ab - 2)3a2b2 - 4ab - 4
     -(3a2b2 - 6ab)
               2ab - 4

Multiply the 2 through the divisor ab - 2:

2(ab - 2) = 2ab - 4

Subtract the 2ab - 4 from the 2ab - 4:

      3ab + 2         
ab - 2)3a2b2 - 4ab - 4
     -(3a2b2 - 6ab)
               2ab - 4
             -(2ab - 4)
                  0

So the result of the division:

(3a2b2 - 4ab - 4)/(ab - 2) = 3ab + 2