3x+1
Stepbystep explanation:
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of
0
.
x

5
3
x
2

14
x

5
Divide the highest order term in the dividend
3
x
2
by the highest order term in divisor
x
.
3
x
x

5
3
x
2

14
x

5
Multiply the new quotient term by the divisor.
3
x
x

5
3
x
2

14
x

5
+
3
x
2

15
x
The expression needs to be subtracted from the dividend, so change all the signs in
3
x
2
−
15
x
3
x
x

5
3
x
2

14
x

5

3
x
2
+
15
x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3
x
x

5
3
x
2

14
x

5

3
x
2
+
15
x
+
x
Pull the next terms from the original dividend down into the current dividend.
3
x
x

5
3
x
2

14
x

5

3
x
2
+
15
x
+
x

5
Divide the highest order term in the dividend
x
by the highest order term in divisor
x
.
3
x
+
1
x

5
3
x
2

14
x

5

3
x
2
+
15
x
+
x

5
Multiply the new quotient term by the divisor.
3
x
+
1
x

5
3
x
2

14
x

5

3
x
2
+
15
x
+
x

5
+
x

5
The expression needs to be subtracted from the dividend, so change all the signs in
x
−
5
3
x
+
1
x

5
3
x
2

14
x

5

3
x
2
+
15
x
+
x

5

x
+
5
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3
x
+
1
x

5
3
x
2

14
x

5

3
x
2
+
15
x
+
x

5

x
+
5
0
Since the remander is
0
, the final answer is the quotient.
3
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

5
3
x
2

14
x

5
Divide the highest order term in the dividend
3
x
2
by the highest order term in divisor
x
.
3
x
x

5
3
x
2

14
x

5
Multiply the new quotient term by the divisor.
3
x
x

5
3
x
2

14
x

5
+
3
x
2

15
x
The expression needs to be subtracted from the dividend, so change all the signs in
3
x
2
−
15
x
3
x
x

5
3
x
2

14
x

5

3
x
2
+
15
x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3
x
x

5
3
x
2

14
x

5

3
x
2
+
15
x
+
x
Pull the next terms from the original dividend down into the current dividend.
3
x
x

5
3
x
2

14
x

5

3
x
2
+
15
x
+
x

5
Divide the highest order term in the dividend
x
by the highest order term in divisor
x
.
3
x
+
1
x

5
3
x
2

14
x

5

3
x
2
+
15
x
+
x

5
Multiply the new quotient term by the divisor.
3
x
+
1
x

5
3
x
2

14
x

5

3
x
2
+
15
x
+
x

5
+
x

5
The expression needs to be subtracted from the dividend, so change all the signs in
x
−
5
3
x
+
1
x

5
3
x
2

14
x

5

3
x
2
+
15
x
+
x

5

x
+
5
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
3
x
+
1
x

5
3
x
2

14
x

5

3
x
2
+
15
x
+
x

5

x
+
5
0
Since the remander is
0
, the final answer is the quotient.
3
x
+
1