Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of
0
.
2
x
-
3
2
x
2
-
3
x
+
5
Divide the highest order term in the dividend
2
x
2
by the highest order term in divisor
2
x
.
x
2
x
-
3
2
x
2
-
3
x
+
5
Multiply the new quotient term by the divisor.
x
2
x
-
3
2
x
2
-
3
x
+
5
+
2
x
2
-
3
x
The expression needs to be subtracted from the dividend, so change all the signs in
2
x
2
−
3
x
x
2
x
-
3
2
x
2
-
3
x
+
5
-
2
x
2
+
3
x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x
2
x
-
3
2
x
2
-
3
x
+
5
-
2
x
2
+
3
x
0
Pull the next term from the original dividend down into the current dividend.
x
2
x
-
3
2
x
2
-
3
x
+
5
-
2
x
2
+
3
x
0
+
5
The final answer is the quotient plus the remainder over the divisor.
x
+
5
2
x
−
3