Step 1
Write down the first coefficient without changes:
β3223β10β3
β3
2
3β10β3
2
Step 2
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
β3223(β3)β
2=β63+(β6)=β3β10β3
β
3
2
3
β10β3
(
β
3
)
β
2
=
β
6
2
3
+
(
β
6
)
=
β
3
Step 3
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
β3223β6β3β10(β3)β
(β3)=9(β10)+9=β1β3
β
3
23
β
10
β3 β6
(
β
3
)
β
(
β
3
)
=
9
2
β
3
(
β
10
)
+
9
=
β
1
Step 4
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
β3223β6β3β109β1β3(β3)β
(β1)=3(β3)+3=0
β
3
23β10
β
3
β69
(
β
3
)
β
(
β
1
)
=
3
2β3
β
1
(
β
3
)
+
3
=
0
We have completed the table and have obtained the following resulting coefficients: 2,β3,β1,0
2
,
β
3
,
β
1
,
0
.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
Thus, the quotient is 2x2β3xβ1
2
x
2
β
3
x
β
1
, and the remainder is 0
0
.
Therefore, 2x3+3x2β10xβ3x+3=2x2β3xβ1+0x+3=2x2β3xβ1
2
x
3
+
3
x
2
β
10
x
β
3
x
+
3
=
2
x
2
β
3
x
β
1
+
0
x
+
3
=
2
x
2
β
3
x
β
1
2x3+3x2β10xβ3x+3=2x2β3xβ1+0x+3=2x2β3xβ1