1. Dividing a Polynomial
By a Monomial
Lesson 27(2)

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.

3. 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

4. - = + = Simplify 3b3 – 6b2 + 9b 6b 3b3 6b 6b2 6b 9b 6b b2 2 3 2 - b +
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 +

5. 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.

6. = = = Example 5x2 – 10x 5 5(x2 – 2x) 5 5(x2 – 2x) 5 x2 – 2x
Factored the numerator. GCF = 5 =
The 5 in the numerator cancels out the 5 in the denominator.
5(x2 – 2x) 5 = =
x2 – 2x

7. = = = Example 2 3b3 – 6b2 + 9b 6b 3b(b2 – 2b + 3b) 6b 3b(b2 – 2b + 3b)
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

8. = = = Example 2 3b(b2 – 2b + 3b) 3b(2) (b2 – 2b + 3b) 2 b2 – 2b + 3b
Divide each term in the numerator by the term in the denominator.
b2 – 2b + 3b = 3b 2 = b2 2
- b +
Remember that you can have a fraction in your answer, just reduce.

9. YOU TRY!
FACTOR COMPLETELY
9x2 – 6x 3
12b3 – 18b2 + 36b 6b

10. YOU TRY!
FACTOR COMPLETELY
2x3 – 4x2 + 6x 4x
15x3 – 5x2 + 10x 5x

11. Class work
Complete Lesson 27(2) worksheet