**Division of a Polynomial by a Monomial**

*To divide a polynomial by a monomial, divide each term in the polynomial by the monomial* .

**Examples**

**Example 1**

Divide 15x ^{2} + 10x by 5x.

**Solution 1**

**Example 2**

Divide 6x ^{2} y ^{3} + 12x ^{4} y ^{2} ÷ (-3xy)

**Solution 2**

**Example 3**

Divide 15x ^{3} - 10x ^{2} + 5x by 5.

**Solution 3**

**Division of a Polynomial by a Monomial Practice Problems**

**Practice**

Divide:

1. (21x ^{2} - 14x) ÷ 7x

2. (30x ^{2} + 20x + 15) ÷ 5

3. (18x ^{2} y ^{3} + 12x ^{4} y ^{2} ) ÷ (-6x)

4. (a ^{3} b ^{2} + 2a ^{4} b - 5a ^{2} b ^{2} ) ÷ ab

5. (8x ^{3} y ^{2} z - 12x ^{4} yz ^{2} ) ÷ (-4xyz)

**Answers**

1. 3x - 2

2. 6x ^{2} + 4x + 3

3. -3xy ^{3} - 2x ^{3} y ^{2}

4. a ^{2} b + 2a ^{3} - 5ab

5. -2x ^{2} y + 3x ^{3} z

Practice problems for these concepts can be found at: Operations with Monomials and Polynomials Practice Test.

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