College Algebra & Trigonometry, 2018a

118 CHAPTER 2. POLYNOMIAL AND RATIONAL FUNCTIONS
Now we’re working with this:
A = B ∗ Q + R
2x 4 +7x 3 +4x 2 − 2x − 1=(x 2 +3x +1)∗ (2x 2 +?+?)+?
But the 2x 2 doesn’t just get multiplied by the x 2 , it will also get multiplied by the
3x and the 1. So now we have:
A = B ∗ Q + R
2x 4 +7x 3 +4x 2 − 2x − 1=(x 2 +3x +1)∗ (2x 2 +?+?)+?
=2x 4 +6x 3 +2x 2 +?????
The issue this raises is that the next multiplication (? ∗ x 2 +? ∗ 3x+? ∗ 1) needs to
add only 1x 3 to our answer, because we need 7x 3 and we already have 6x 3 from
the previous multiplication. That means we’re going to want to multiply next by
1x:
A = B ∗ Q + R
2x 4 +7x 3 +4x 2 − 2x − 1=(x 2 +3x +1)∗ (2x 2 +1x+?)+?
=2x 4 +6x 3 +2x 2
= 1x 3 +3x 2 + x
=2x 4 +7x 3 +5x 2 +1x+???
In the next round of mutiplication, we’re going to want to bring the 5x 2 down to
4x 2 , so we’ll need to multiply by −1.