College Algebra & Trigonometry, 2018a

2.6. POLYNOMIAL LONG DIVISION 117
Now we need to determine how many times 38 will divide into 11,462. We decided
on 300 ∗ 38 = 11, 400, then we subtract to see how much is left over:
11, 462
−11, 400
00, 062
We can see that we won’t need any tens in our answer, and that 38 divides into 62
one time with 24 left over, thus the answer is 2 thousands, 3 hundreds, no tens, 1
and a remainder of 24. To check the answer, we multiply 38 ∗ 2301 and add 24:
2, 301
×38
18408
6903
87438
+24
87462
Polynomial long division works in much the same way that numerical long division
does. Given a problem A ÷ B, the goal is to find a quotient Q and remainder
R so that A = B ∗ Q + R.
Let’s look at this with the example 2x 4 +7x 3 +4x 2 − 2x − 1 ÷ x 2 +3x +1or:
2x 4 +7x 3 +4x 2 − 2x − 1
x 2 +3x +1
So, we are looking to answer the question:
A = B ∗ Q + R
2x 4 +7x 3 +4x 2 − 2x − 1=(x 2 +3x +1)∗ (?+?+?)+?
If we want to mulitply x 2 +3x +1times something and end up with 2x 4 +7x 3 +
4x 2 − 2x − 1, then what we multiply by is going to have to start with 2x 2 , because
x 2 ∗ 2x 2 =2x 4 .