College Algebra & Trigonometry, 2018a

128 CHAPTER 2. POLYNOMIAL AND RATIONAL FUNCTIONS
Next, −4 ∗−3 = +12:
−3 3 5 −9 9
↓ −9 12
3 −4 3
And this example also has a zero remainder:
The answer here is 3x 2 − 4x +3:
−3 3 5 −9 9
↓ −9 12 −9
3 −4 3 0
3x 3 +5x 2 − 9x +9
x +3
=3x 2 − 4x +3
and
3x 3 +5x 2 − 9x +9=(x + 3)(3x 2 − 4x +3)
Let’s look at an example that is a little bit different.
Example
Use Synthetic Division to divide:
6x 4 + x 3 +9x 2 + x − 2
2x +1
Synthetic Division is set up to handle problems in which we are dividing by
1x − a. Clearly, this is not the case in this example, however we can work around
this. Another way of looking at setting up the synthetic division is that we use
the number that is the solution to x − a =0. When we divided by x − 5, we used
+5. When we were dividing by x +3, we used −3. So, if we’re going to divide by
2x +1, we’ll use − 1 in the Synthetic Division:
2
− 1 2
6 1 9 1 −2
↓
6