College Algebra & Trigonometry, 2018a

2.7. SYNTHETIC DIVISION 127
In the last step, multiply the 1 times the 5 and combine the result with the −5 in
the problem to get zero:
5 2 −6 −23 16 −5
↓ +10 +20 −15 5
2 4 −3 1 0
This last coefficient represents the remainder - in this case 0. The other numerals
in the answer represent the coefficients for the powers of x in the answer. On the
far right is the remainder, then the constant (x 0 ) term, then the linear (x 1 ) term
and so on:
5 2 −6 −23 16 −5
↓ +10 +20 −15 5
2x 3 4x 2 −3x 1 1x 0 0
2x 4 − 6x 3 − 23x 2 +16x − 5
x − 5
=2x 3 +4x 2 − 3x +1
Let’s look at another example:
Example
Use Synthetic Division to divide:
3x 3 +5x 2 − 9x +9
x +3
Since Synthetic Division is set up to divide by x − a, if we’re dividing by x +3
we’ll need to use a −3 in the Synthetic Division:
Then, 3 ∗−3=−9:
−3 3 5 −9 9
↓
3
−3 3 5 −9 9
↓ −9
3 −4