# Divide a Polynomial by a Monomial

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

## Example 1

### Example

### Solution

Solve 5x^{2}/x.

See the coefficients.

5/1 = 5

So write 5.

See the variable x.

x^{2}/x = x^{2 - 1} = x^{1} = x

So write x.

Quotient of Powers

So 5x^{2}/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

### Example

### Solution

Solve 12x^{2}y/2xy.

See the coefficients.

12/2 = 6

So write 6.

See the variable x.

x^{2}/x = x^{2 - 1} = x^{1} = x

So write x.

See the variable y.

y/y

Both y are cancelled.

So 12x^{2}y/2xy = 6x.

Solve +4xy^{3}/2xy.

See the coefficients.

+4/2 = +2

So write +2.

See the variable x.

x/x

Both x are cancelled.

See the variable y.

y^{3}/y = y^{3 - 1} = y^{2}

So write y^{2}.

So +4xy^{3}/2xy = +2y^{2}.

So 6x + 2y^{2} is the answer.

## Example 3

### Example

### Solution

Solve 6x^{5}/3x^{2}.

See the coefficients.

6/3 = 2

So write 2.

See the variable x.

x^{5}/x^{2} = x^{5 - 2} = x^{3}

So write x^{3}.

So 6x^{5}/3x^{2} = 2x^{3}.

Solve +3x^{4}/3x^{2}.

See the coefficients.

+3/3 = +1

So write +.

See the variable x.

x^{4}/x^{2} = x^{4 - 2} = x^{2}

So write x^{2}.

So +3x^{4}/3x^{2} = +x^{2}.

Solve -12x^{2}/3x^{2}.

See the coefficients.

-12/3 = -4

So write -4.

See the variable x.

x^{2}/x^{2}

Both x^{2} are cancelled.

So -12x^{2}/3x^{2} = -4.

So 2x^{3} + x^{2} - 4 is the answer.