Dividing Polynomials

A polynomial looks like this:

polynomial example
example of a polynomial
this one has 3 terms

Dividing

Sometimes it is easy to divide a polynomial by splitting it at the "+" and "-" signs, like this (press play):

When the polynomial was split into two parts we still had to keep the "/3" under each one.

Then the highlighted parts were "reduced" (6/3 = 2 and 3/3 = 1) to leave the answer of 2x-1

Here is another, slightly more complicated, example:

What happened?

  • The 1st Term had x2 above and x below, which together becomes just x
  • The 2nd Term had x above and below, so they canceled each other out
  • We couldn't simplify "1/3x" any further.

That is as far as we can get. But the answer is still "simpler"

Note: the result is a valid answer but is not a polynomial, because the last term (1/3x) has division by a variable (x).

 

Now, sometimes it helps to rearrange the top polynomial before dividing, as in this example:

Long Division

If none of those methods work, we may need to use Polynomial Long Division.