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How to divide polynomials by binomials step by step

Dividing polynomials by a binomial is simple.

The following example will help you to divide polynomials by binomials.

We will explain how to divide a polynomial by a binomial step by step.

Dividing a polynomial by a binomial

Simple example.

We will divide the polynomial 2x2 + x - 3 by the binomial x - 1:

(2x2 + x - 3)/(x - 1)

The 2x2 + x - 3 is a dividend and the x - 13 is a divisor.

We use the long division symbol:

                 
x - 1)2x2 + x - 3

To begin let's divide the first term of the dividend (the 2x2) by the first term of the divisor (the x):

2x2/x = 2x

Put the result 2x over the long division symbol:

      2x          
x - 1)2x2 + x - 3

Multiply the 2x through the divisor x - 1:

2x(x - 1) = 2x2 - 2x

Subtract the 2x2 - 2x from the two leading terms of the dividend:

      2x          
x - 1)2x2 + x - 3
    -(2x2 - 2x)
            3x

Carry down the last dividend term:

      2x          
x - 1)2x2 + x - 3
    -(2x2 - 2x)
            3x - 3

Divide the first term of the 3x - 3 (the 3x) by the first term of the divisor (the x):

3x/x = 3

Put the result 3 over the long division symbol:

      2x + 3     
x - 1)2x2 + x - 3
    -(2x2 - 2x)
            3x - 3

Multiply the 3 through the divisor x - 1:

3(x - 1) = 3x - 3

Subtract the 3x - 3 from the 3x - 3:

      2x + 3     
x - 1)2x2 + x - 3
    -(2x2 - 2x)
            3x - 3
          -(3x - 3)
               0

So the result of the division:

(2x2 + x - 3)/(x - 1) = 2x + 3