Question

x^4-1 divided by x^2-1​

Answer 1

(
x
4
−
1
)
(
x
2
−
1
)
(
x
4
-
1
)
(
x
2
-
1
)
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of
0
0
.
x
2
x
2
+
0
x
0
x
-
1
1
x
4
x
4
+
0
x
3
0
x
3
+
0
x
2
0
x
2
+
0
x
0
x
-
1
1
Divide the highest order term in the dividend
x
4
x
4
by the highest order term in divisor
x
2
x
2
.
x
2
x
2
x
2
x
2
+
0
x
0
x
-
1
1
x
4
x
4
+
0
x
3
0
x
3
+
0
x
2
0
x
2
+
0
x
0
x
-
1
1
Multiply the new quotient term by the divisor.
x
2
x
2
x
2
x
2
+
0
x
0
x
-
1
1
x
4
x
4
+
0
x
3
0
x
3
+
0
x
2
0
x
2
+
0
x
0
x
-
1
1
+
x
4
x
4
+
0
0
-
x
2
x
2
The expression needs to be subtracted from the dividend, so change all the signs in
x
4
+
0
−
x
2
x
4
+
0
-
x
2
x
2
x
2
x
2
x
2
+
0
x
0
x
-
1
1
x
4
x
4
+
0
x
3
0
x
3
+
0
x
2
0
x
2
+
0
x
0
x
-
1
1
-
x
4
x
4
-
0
0
+
x
2
x
2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x
2
x
2
x
2
x
2
+
0
x
0
x
-
1
1
x
4
x
4
+
0
x
3
0
x
3
+
0
x
2
0
x
2
+
0
x
0
x
-
1
1
-
x
4
x
4
-
0
0
+
x
2
x
2
+
x
2
x
2
Pull the next term from the original dividend down into the current dividend.
x
2
x
2
x
2
x
2
+
0
x
0
x
-
1
1
x
4
x
4
+
0
x
3
0
x
3
+
0
x
2
0
x
2
+
0
x
0
x
-
1
1
-
x
4
x
4
-
0
0
+
x
2
x
2
+
x
2
x
2
+
0
x
0
x
-
1
1
Divide the highest order term in the dividend
x
2
x
2
by the highest order term in divisor
x
2
x
2
.
x
2
x
2
+
0
x
0
x
+
1
1
x
2
x
2
+
0
x
0
x
-
1
1
x
4
x
4
+
0
x
3
0
x
3
+
0
x
2
0
x
2
+
0
x
0
x
-
1
1
-
x
4
x
4
-
0
0
+
x
2
x
2
+
x
2
x
2
+
0
x
0
x
-
1
1
Multiply the new quotient term by the divisor.
x
2
x
2
+
0
x
0
x
+
1
1
x
2
x
2
+
0
x
0
x
-
1
1
x
4
x
4
+
0
x
3
0
x
3
+
0
x
2
0
x
2
+
0
x
0
x
-
1
1
-
x
4
x
4
-
0
0
+
x
2
x
2
+
x
2
x
2
+
0
x
0
x
-
1
1
+
x
2
x
2
+
0
0
-
1
1
The expression needs to be subtracted from the dividend, so change all the signs in
x
2
+
0
−
1
x
2
+
0
-
1
x
2
x
2
+
0
x
0
x
+
1
1
x
2
x
2
+
0
x
0
x
-
1
1
x
4
x
4
+
0
x
3
0
x
3
+
0
x
2
0
x
2
+
0
x
0
x
-
1
1
-
x
4
x
4
-
0
0
+
x
2
x
2
+
x
2
x
2
+
0
x
0
x
-
1
1
-
x
2
x
2
-
0
0
+
1
1
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x
2
x
2
+
0
x
0
x
+
1
1
x
2
x
2
+
0
x
0
x
-
1
1
x
4
x
4
+
0
x
3
0
x
3
+
0
x
2
0
x
2
+
0
x
0
x
-
1
1
-
x
4
x
4
-
0
0
+
x
2
x
2
+
x
2
x
2
+
0
x
0
x
-
1
1
-
x
2
x
2
-
0
0
+
1
1
0
0
Since the remander is
0
0
, the final answer is the quotient.
x
2
+
0
x
+
1