# Divide a Polynomial by a Monomial

How to divide a polynomial by a monomial: 3 examples and their solutions.

## Example 1

### Solution

Solve 5x2/x.

See the coefficients.
5/1 = 5
So write 5.

See the variable x.
x2/x = x2 - 1 = x1 = x
So write x.

Quotient of Powers

So 5x2/x = 5x.

Solve -3x/x.

See the coefficients.
-3/1 = -3
So write -3.

See the variable x.
x/x
Both x are cancelled.

So -3x/x = -3.

So 5x - 3 is the answer.

## Example 2

### Solution

Solve 12x2y/2xy.

See the coefficients.
12/2 = 6
So write 6.

See the variable x.
x2/x = x2 - 1 = x1 = x
So write x.

See the variable y.
y/y
Both y are cancelled.

So 12x2y/2xy = 6x.

Solve +4xy3/2xy.

See the coefficients.
+4/2 = +2
So write +2.

See the variable x.
x/x
Both x are cancelled.

See the variable y.
y3/y = y3 - 1 = y2
So write y2.

So +4xy3/2xy = +2y2.

So 6x + 2y2 is the answer.

## Example 3

### Solution

Solve 6x5/3x2.

See the coefficients.
6/3 = 2
So write 2.

See the variable x.
x5/x2 = x5 - 2 = x3
So write x3.

So 6x5/3x2 = 2x3.

Solve +3x4/3x2.

See the coefficients.
+3/3 = +1
So write +.

See the variable x.
x4/x2 = x4 - 2 = x2
So write x2.

So +3x4/3x2 = +x2.

Solve -12x2/3x2.

See the coefficients.
-12/3 = -4
So write -4.

See the variable x.
x2/x2
Both x2 are cancelled.

So -12x2/3x2 = -4.

So 2x3 + x2 - 4 is the answer.