Dividing Polynomials
When you add fractions, you get a common denominator, then
combine the tops. The same goes for subtraction.  . By the same token,  , etc. I can break it up anyway that is
convenient, as long as the denominators are the same and the tops
add up to the right thing.
Example:
 . By the same token,  , etc.
I can break it up anyway that is convenient, as long as the
denominators are the same and the tops add up to the right thing.
- When you have a monomial over a monomial, you simplify:
Example:
New Stuff:
- To divide a polynomial by a monomial, we use the
principles discussed above to break up the polynomial on
top into monomials and simplify each.
Example:
- To check your answer after doing a by (polynomial you are
dividing by).
- Long division of polynomials. DESPITE WHAT THE BOOK
IMPLIES, IT IS NOT NECESSARY FOR THE DIVISOR TO BE A
BINOMIAL FOR THIS METHOD TO WORK.
Recall:
Long division of whole numbers.
Example:
Use long division to compute 3249 ÷ 23.
New Stuff:
- With numbers, we write them so that the position of each
digit is important. Thus, if you have no tens in a given
number, you put a “0” in the tens place. With
polynomials, the “places” are the powers of the
variable(s). If we don’t have any x 2’s,
then we don’t write the x 2 term. This
can cause a problem when trying to line things up in
columns. Thus, if the dividend (polynomial under the
guzzinta) is missing terms, we fill them in with a
coefficient of 0. In other words, if there is no x 2
term, we write “0 x 2 ” where an x 2
term should be. We also put in a constant term of
“0” if there is none.
Example:
Put in any necessary placeholders: 
Other than the little twist of placeholders, division of
polynomials division of whole numbers.
Write your answers in the form
Example:
Divide (2x 3 - 5x 2 + 5x - 4) ÷ (2x +
1).
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