1. Greatest Common Factor December 2, 2014 Pages 42 – 43 in Notes

2. Warm-Up What do the following have in common? 3 and 12 x and x 2 5x 2 and 20x 5

3. Objective solve quadratic equations and inequalities using graphs, tables, and algebraic methods.[8.D]

4. Essential Question What is the greatest common factor and how does it relate to quadratic functions?

5. What is factoring by the GCF? The biggest number and highest power of a variable that can be divided out of all terms. Whatever you can take out goes to the front of the parentheses. Your answer should look like a distribution problem.

6. Example 1 3x 2 + 6x  What is the biggest number that will divide out of each number? 33  What is the highest power of a variable that can be divided out of each term? x1x1 So, our factored form is: 3x(x + 2)

7. Example 2 25y 3 – 30y 2  What is the biggest number that will divide out of each number? 55  What is the highest power of a variable that can be divided out of each term? y2y2 So, our factored form is: 5y 2 (5y – 6)

8. Example 3 -6x 3 – 4x 2 + 8  What is the biggest number that will divide out of each number?  -2 (ALWAYS factor out the negative)  What is the highest power of a variable that can be divided out of each term?  There isn’t one since 8 doesn’t have a variable. So, our factored form is: -2(3x 3 + 2x 2 – 4)

9. Example 4 -6x 3 + 15x 2 + 11x  What is the biggest number that will divide out of each number?  -1  What is the highest power of a variable that can be divided out of each term? x1x1 So, our factored form is: -x(6x 2 – 15x – 11)

10. Assignment 1.x 2 – 2x 2.5x 3 + 10x 2 – 15x + 5 3.–3x 3 + 6x 2 – 9x 4.25x 2 + 125 5.8x 3 + 12x – 4 6.–2x 2 + 4x – 8

11. Reflection Explain to your partner in your own words what greatest common factor is.