Answer: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
4
x
2
-
2
x
-
5
Divide the highest order term in the dividend
4
x
2
by the highest order term in divisor
x
.
4
x
x
+
1
4
x
2
-
2
x
-
5
Multiply the new quotient term by the divisor.
4
x
x
+
1
4
x
2
-
2
x
-
5
+
4
x
2
+
4
x
The expression needs to be subtracted from the dividend, so change all the signs in
4
x
2
+
4
x
4
x
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
4
x
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
-
6
x
Pull the next terms from the original dividend down into the current dividend.
4
x
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
-
6
x
-
5
Divide the highest order term in the dividend
−
6
x
by the highest order term in divisor
x
.
4
x
-
6
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
-
6
x
-
5
Multiply the new quotient term by the divisor.
4
x
-
6
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
-
6
x
-
5
-
6
x
-
6
The expression needs to be subtracted from the dividend, so change all the signs in
−
6
x
−
6
4
x
-
6
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
-
6
x
-
5
+
6
x
+
6
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
4
x
-
6
x
+
1
4
x
2
-
2
x
-
5
-
4
x
2
-
4
x
-
6
x
-
5
+
6
x
+
6
+
1
The final answer is the quotient plus the remainder over the divisor.
4
x
−
6
+
1
x
+
1
Step-by-step explanation:
