1. Chapter 6 – Polynomials and Polynomial Functions
6.4 – Multiplying and Dividing Polynomials

2. 6.4 – Multiplying and Dividing Polynomials
Today we will be learning how to:
Multiply and divide polynomials

3. 6.4 – Multiplying and Dividing Polynomials
To multiply two polynomials, you multiply each term of the first polynomial by each term of the second polynomial.
You can use a vertical or a horizontal format.

4. 6.4 – Multiplying and Dividing Polynomials
Example 1 - vertically
Find the product of (3x2 + 3x + 5)(2x + 3)

5. 6.4 – Multiplying and Dividing Polynomials
Example 2 - horizontally
Find the product of
(x – 5)(x2 – 2x + 3)
(x + 3)(x – 4)(x + 5)

6. 6.4 – Multiplying and Dividing Polynomials
Special Products
Sum and Difference
(a + b)(a – b) = a2 – b2
(x + 4)(x – 4) = x2 – 16
Square of a binomial
(a + b)2 = a2 + 2ab + b2
(x + 3)2 = x2 + 6x + 9
(a – b)2 = a2 – 2ab + b2
(3x – 4)2 = 9x2 – 24x + 16

7. 6.4 – Multiplying and Dividing Polynomials
Special Products continued
Cube of a binomial
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(x + 2)3 = x3 + 6x2 + 12x + 8
(a – b)3 = a3 – 3a2b + 3ab2 – b3
(x – 2)3 = x3 – 6x2 + 12x – 8

8. 6.4 – Multiplying and Dividing Polynomials
Example 3
Find the product of (5y – 3)(5y + 3)

9. 6.4 – Multiplying and Dividing Polynomials
Example 4
Find the product of (4a + 7)2

10. 6.4 – Multiplying and Dividing Polynomials
Example 5
Find the product of (m – 6)3

11. 6.4 – Multiplying and Dividing Polynomials
HOMEWORK 6.4 Worksheet #1 - 18

12. 6.4 – Multiplying and Dividing Polynomials
You can divide polynomials using polynomial long division
You follow the same steps to divide polynomials as you do to divide whole numbers
divide, multiply, subtract and bring down
Before dividing polynomials, make sure the dividend and divisor are in standard form

13. 6.4 – Multiplying and Dividing Polynomials
Example 6
Find the quotient of 875 ÷ 31

14. 6.4 – Multiplying and Dividing Polynomials
Example 7
Find the quotient of (3x3 + 17x2 + 21x – 11) ÷ (x + 3)

15. 6.4 – Multiplying and Dividing Polynomials
HOMEWORK 6.4 Worksheet #21 – 29