To divide a polynomial by a monomial, first identify which one is which. Then, separate the division into parts. Finally, once each part is processed, put them back together.
- Figure out which is the polynomial and which is the monomial
An algebraic expression with just one term is called a monomial. That could be a variable, number, or a number attached with a variable. For example x and y are both variables, 11 and 12 are numbers, and 3x and -8xy are numbers attached to variables. A polynomial is an expression with more than one term, all joined by either a plus or minus sign. For example, 6x+6y and 7x+3xy+z+5 are both polynomials
- Split the operation into parts.
Process each term of the polynomial by the single term of the monomial. For example, if dividing 3xy+9x+12 by 3, the first operation would be 3xy divided by 3. The answer is xy. Then, 9x should be divided by 3, getting 3x. Finally, 12 would be divided by 3, getting 4.
- Put the parts back together
Once the parts have been divided, it's time to put them back again. Simply connect the divisions from the previous step by the original operation that connected them, either a plus or minus sign. To continue the example from the previous step, the answer would be xy+3x+4.