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# Dividing a Polynomial By a Monomial PowerPoint PPT Presentation

Dividing a Polynomial By a Monomial. Lesson 27(2). Things to Remember. When dividing Polynomials by a monomial, remember to divide each term in the numerator by the term in the denominator .

Dividing a Polynomial By a Monomial

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#### Presentation Transcript

Dividing a Polynomial

By a Monomial

Lesson 27(2)

### Things to Remember

• When dividing Polynomials by a monomial, remember to divide each term in the numerator by the term in the denominator.

• Remember your exponent laws for dividing. You subtract the exponents if the base is the same.

• Remember your answer can have a fraction. You may only have to reduce the fraction in some cases.

### Simplify

• When Dividing a Polynomial by a monomial, you are simplifying the expression.

5x2 – 10x

5

Simplify,

Divide each term in the numerator by the term in the denominator.

5x2

5

10x

5

-

=

=

x2 – 2x

### Simplify

• When Dividing a Polynomial by a monomial, you are simplifying the expression.

3b3 – 6b2 + 9b

6b

Simplify,

Divide each term in the numerator by the term in the denominator.

3b3

6b

6b2

6b

9b

6b

-

=

+

b2

2

3

2

=

Remember that you can have a fraction in your answer, just reduce.

- b +

### Second Method

• There is another way to divide a polynomial by a monomial.

• We factor the polynomial, and then divide the monomial into the common factor.

• If necessary, we factor the monomial before dividing.

### Example

5x2 – 10x

5

5(x2 – 2x)

5

Factored the numerator. GCF = 5

=

The 5 in the numerator cancels out the 5 in the denominator.

5(x2 – 2x)

5

=

=

x2 – 2x

### Example 2

3b3 – 6b2 + 9b

6b

Factored the numerator. GCF = 3b

3b(b2 – 2b + 3b)

6b

=

Factored the monomial in the denominator.

3b(b2 – 2b + 3b)

3b(2)

=

The 3b in the numerator cancels out the 3b in the denominator.

3b(b2 – 2b + 3b)

3b(2)

=

Continued next slide

### Example 2

3b(b2 – 2b + 3b)

3b(2)

(b2 – 2b + 3b)

2

=

Divide each term in the numerator by the term in the denominator.

b2 – 2b + 3b

2 2 2

=

3b

2

=

b2

2

- b +

Remember that you can have a fraction in your answer, just reduce.

YOU TRY!

FACTOR COMPLETELY

9x2 – 6x

3

12b3 – 18b2 + 36b

6b

YOU TRY!

FACTOR COMPLETELY

2x3 – 4x2 + 6x

4x

15x3 – 5x2 + 10x

5x

### Class work

• Complete Lesson 27(2) worksheet