A polynomial looks like this:
|example of a polynomial
this one has 3 terms
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:
- 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:
If none of those methods work, we may need to use Polynomial Long Division.