Solution
Step 1 Write the problem in long division form.

Algebra 

The terms of each polynomial
are in descending order. 


Step 2 Divide the first term of the dividend by the first term of the
divisor. 
Hereâ€™s a long division problem from
arithmetic to help you see the similarities
between the algebra and the arithmetic. 
Divide 6x^{3} by 2x to get 3x^{2}.
Write 3x^{2} in the quotient
line above 7x^{2}, the x^{2}term
of the dividend. 


Step 3 Multiply the divisor by the term you found in Step 2. 

Multiply (2x + 1) by 3x^{2} to
get 6x^{3} + 3x^{2}. 


Step 4 Subtract the expression you found in Step 3 from the dividend. 

Subtract (6x^{3} + 3x^{2}) from (6x^{3}
+ 7x^{2}). The result is 4x^{2}. 


Step 5 Bring down the next term from the dividend.


Write + 4x to the right of 4x^{2}. 


Step 6 Repeat Steps 2 through 5 until the degree of the remainder is less
than the degree of the divisor. 

Divide 4x^{2} by 2x to get 2x.
Write 2x in the quotient line. Multiply (2x + 1) by 2x to
get 4x^{2} + 2x. Subtract (4x^{2} + 2x) from (4x^{2}
+ 4x). The result is 2x.
Write 2 to the right of 2x. 


Divide 2x by 2x to get 1.
Write +1 in the quotient line.
Multiply (2x + 1) by 1 to get 2x + 1.
Subtract (2x + 1) from (2x  2).
The result is 3. 


The degree of the remainder,
3, is less than the degree of the divisor,
2x + 1. So we stop. 
Step 7 Write the quotient. The quotient is:


Quotient is
