Division of a polynomial by a monomial

 7x3y2 - 21x2y + 35x3y4
————————————————————————
       7x2y

There are three terms in the numerator. Therefore write
a row of lines and signs, using the signs between the
terms of the numerator


——————— - ——————— + ————————

Then write the terms in order above the lines:

 7x3y2     21x2y     35x3y4
——————— - ——————— + ————————

Then write the denominator under each line: 


 7x3y2     21x2y     35x3y4
——————— - ——————— + ————————
 7x2y      7x2y       7x2y

Now you have three problems to solve

In the first, cancel the 7's, subtract the exponents of x
any y, and get xy

          21x2y     35x3y4
    xy - ——————— + ————————
          7x2y       7x2y 

In the second divide 21 by 7 getting 3. Cancel the x2's
and the y, getting just 3.

                    35x3y4
          xy - 3 + ————————
                     7x2y

In the third, divide 35 by 7, getting 5. Subtract the 
exponents of the x's, and the y's, getting 5xy3

                    
          xy - 3 + 5xy3

Edwin
AnlytcPhil@aol.com