x-1/x^3-1
Division by long division method
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Algebra Examples
Popular Problems Algebra Divide Using Long Polynomial Division (x^3-1)÷(x-1)
(
x
3
−
1
)
÷
(
x
−
1
)
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of
0
.
x
-
1
x
3
+
0
x
2
+
0
x
-
1
Divide the highest order term in the dividend
x
3
by the highest order term in divisor
x
.
x
2
x
-
1
x
3
+
0
x
2
+
0
x
-
1
Multiply the new quotient term by the divisor.
x
2
x
-
1
x
3
+
0
x
2
+
0
x
-
1
+
x
3
-
x
2
The expression needs to be subtracted from the dividend, so change all the signs in
x
3
−
x
2
x
2
x
-
1
x
3
+
0
x
2
+
0
x
-
1
-
x
3
+
x
2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x
2
x
-
1
x
3
+
0
x
2
+
0
x
-
1
-
x
3
+
x
2
+
x
2
Pull the next terms from the original dividend down into the current dividend.
x
2
x
-
1
x
3
+
0
x
2
+
0
x
-
1
-
x
3
+
x
2
+
x
2
+
0
x
Divide the highest order term in the dividend
x
2
by the highest order term in divisor
x
.
x
2
+
x
x
-
1
x
3
+
0
x
2
+
0
x
-
1
-
x
3
+
x
2
+
x
2
+
0
x
Multiply the new quotient term by the divisor.
x
2
+
x
x
-
1
x
3
+
0
x
2
+
0
x
-
1
-
x
3
+
x
2
+
x
2
+
0
x
+
x
2
-
x
The expression needs to be subtracted from the dividend, so change all the signs in
x
2
−
x
x
2
+
x
x
-
1
x
3
+
0
x
2
+
0
x
-
1
-
x
3
+
x
2
+
x
2
+
0
x
-
x
2
+
x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x
2
+
x
x
-
1
x
3
+
0
x
2
+
0
x
-
1
-
x
3
+
x
2
+
x
2
+
0
x
-
x
2
+
x
+
x
Pull the next terms from the original dividend down into the current dividend.
x
2
+
x
x
-
1
x
3
+
0
x
2
+
0
x
-
1
-
x
3
+
x
2
+
x
2
+
0
x
-
x
2
+
x
+
x
-
1
Divide the highest order term in the dividend
x
by the highest order term in divisor
x
.
x
2
+
x
+
1
x
-
1
x
3
+
0
x
2
+
0
x
-
1
-
x
3
+
x
2
+
x
2
+
0
x
-
x
2
+
x
+
x
-
1
Multiply the new quotient term by the divisor.
x
2
+
x
+
1
x
-
1
x
3
+
0
x
2
+
0
x
-
1
-
x
3
+
x
2
+
x
2
+
0
x
-
x
2
+
x
+
x
-
1
+
x
-
1
The expression needs to be subtracted from the dividend, so change all the signs in
x
−
1
x
2
+
x
+
1
x
-
1
x
3
+
0
x
2
+
0
x
-
1
-
x
3
+
x
2
+
x
2
+
0
x
-
x
2
+
x
+
x
-
1
-
x
+
1
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x
2
+
x
+
1
x
-
1
x
3
+
0
x
2
+
0
x
-
1
-
x
3
+
x
2
+
x
2
+
0
x
-
x
2
+
x
+
x
-
1
-
x
+
1
0
Since the remander is
0
, the final answer is the quotient.
x
2
+
x
+
1