College Algebra & Trigonometry, 2018a

126 CHAPTER 2. POLYNOMIAL AND RATIONAL FUNCTIONS
This set-up allows us to complete the division problem 2x4 − 6x 3 − 23x 2 +16x − 5
.
x − 5
5 2 −6 −23 16 −5
The first coefficient in the answer is the same as the first coefficient in the polynomial
we’re dividing into:
5 2 −6 −23 16 −5
↓
2
To get the next coefficient, we multiply the 2 by the 5 to get +10 and flll this in
under the −6:
5 2 −6 −23 16 −5
↓ +10
2
Then, −6+10=+4, which is the next coefficient in the answer:
5 2 −6 −23 16 −5
↓ +10
2 4
Then, we continue this process, multiplying the 4 by the 5 to get 20 and combining
this with the −23: −23+20=−3:
5 2 −6 −23 16 −5
↓ +10 +20
2 4 −3
Next, multiply the −3 by the 5 and combine the resulting −15 with the 16:
5 2 −6 −23 16 −5
↓ +10 +20 −15
2 4 −3 1