1. Alg-2 Lesson 6-1 - Factoring expressions (see section 5-4 (page 353) of the book)

2. Quiz 1. Simplify the following expressions. 2.

3. Power Power: An expression formed by repeated multiplication of the same factor. Coefficient Base Exponent The exponent applies to the number or variable immediately to its left, not to the coefficient !!! to its left, not to the coefficient !!!

4. Your turn: Simplify 3(2x – 1) key concept every term inside the parentheses is multiplied by 3. 1. 3(2x) +3(– 1) 6x – 3

5. Your turn: Simplify (x – 1)(2x + 3) Each term inside the left parentheses is multiplied by every term inside the right parentheses. (x)(2x + 3) – 1(2x + 3) Distributive Property twice 2.

6. Multiplying Polynomials How do you multiply a trinomial and a binomial? Each term inside one set of parentheses is multiplied by every term inside the other parentheses. 3. Multiply the trinomial and the binomial above.

7. Multiplying Polynomials (x – 1)(2x + 3)(3x – 2) = [ (x – 1)(2x + 3) ] (3x – 2) How do you multiply three binomials? Pick 2 factors, multiply them to get a product, then multiply the product by the last factor  associative property. multiply the product by the last factor  associative property. (x – 1)*(2x + 3)*(3x – 2) 11. Multiply the two binomials on the left. (next slide shows process)

8. Multiplying Polynomials (x – 1)(2x + 3)(3x – 2) = [ (x – 1)(2x + 3) ] (3x – 2) How do you multiply three binomials? = [ x(2x + 3) – 1(2x + 3) ] (3x – 2)

9. Your Turn: Simplify ( Multiply the Binomials and combine like terms) 4.

10. Factor the following using Algebra Tiles What is the length? What is the width?

11. What is the length? What is the width? Factor the following using Algebra Tiles

12. What are the factors of:

13. Your Turn: Factor out the “common factor” 5. 6. 7.

14. Factor the following using Algebra Tiles

15. What would the following look like?

16. These go on the ends of the ‘x’ blocks These go on the ends of the ‘x^2’ blocks

17. Two of these Three of these.

20. Check it!

21. Factor out the common factor

22. Your turn: 7. 8.

23. Sometimes you can go further! This can be factored! (remember factoring trinomials?) What two numbers multiplied equals -8, and the same two numbers added together equals 2.

24. If this were an equation, what are the x-intercepts? x-intercepts occur when y = 0 Based upon the zero product property, what values of x make the equation equal to zero?

25. What are these values? What option on the calculator would you use to find them? Option 4 (maximum) Option 3 (minimum)