College Algebra & Trigonometry, 2018a

2.6. POLYNOMIAL LONG DIVISION 121
First, we set up the problem:
x 2 − x +4 ) 3x 4 − 8x 3 +19x 2 − 15x +10
Then, we question: “What do we need to multiply x 2 by to get 3x 4 ?” Answer:
“3x 2 ”
3x 2
x 2 − x +4 ) 3x 4 − 8x 3 +19x 2 − 15x +10
Then, we multiply, change signs (subtract) and combine like terms:
3x 2
x 2 − x +4 ) 3x 4 − 8x 3 +19x 2 − 15x +10
− 3x 4 +3x 3 − 12x 2
− 5x 3
+7x 2 − 15x
Now we’ll need to multiply by −5x, change signs and combine like terms:
3x 2
− 5x
x 2 − x +4 ) 3x 4 − 8x 3 +19x 2 − 15x +10
− 3x 4 +3x 3 − 12x 2
− 5x 3 +7x 2 − 15x
5x 3 − 5x 2 +20x
2x 2 +5x +10
We need 2x 2 so we’ll need to multiply by 2, change signs and combine like terms:
3x 2 − 5x +2
x 2 − x +4 ) 3x 4 − 8x 3 +19x 2 − 15x +10
− 3x 4 +3x 3 − 12x 2
− 5x 3 +7x 2 − 15x
5x 3 − 5x 2 +20x
2x 2 +5x +10
− 2x 2 +2x − 8
7x +2