Dividing a Polynomial By a Monomial

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 • 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 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 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 = 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.

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