2. December 5, 2011 At the end of today, you will be able to factor polynomials. Warm-up: For today’s lesson you need to remember how to find the GCF. 1. What is GCF of 40 and 24? 2.What is GCF of 16x 2 and 8x Questions from Final Review? HW 5.4: Finish 5.4 WS #1-18

3. Lesson 5.4 Factoring Factoring is like backwards distributing… Distribute: 3x(5x – 8) 15x 2 – 24x Now let’s go backwards! Think to yourself “What is the GCF of 15x 2 and 24x?” So 3x goes outside the parentheses and now fill in the blanks. 3x 3x( - ) 15x 2 – 24x = 5x - 8

4. Factor practice! 1. 16x 2 + 8x 8x( + ) Do #1 and #3 on WS 5.4 What’s the GCF? 2x 1 Check your answer by distributing to see if it becomes the problem.

5. “What’s my number?” Guess the two numbers before it leaves the screen…QUICK! Think of two numbers when… …multiplied gives you -30 and add up to 7. …multiplied gives you 24 and add up to 10 …multiplied gives you -21 and add up to -4

6. Factoring when it has the form ax 2 + bx + c, when a = 1 ( )( ) Use the game we just played to factor this: x 2 +10x + 24 Think: “two numbers multiplied to give you 24 that add up to 10” (x + 6)(x + 4) 24 10 64

7. Practice Time! Factor On WS 5.4, do #5, 7, 14 Can x 2 + 81 be factored?

8. Factoring when a ≠ 1 First check that there is no GCF! Example 1: 5x 2 – 13x + 6 Step 1: Multiply a and c 30 Step 2: Factor -13 -10-3 Step 3: Rewrite expression with new factors 5x 2 – 10x – 3x + 6 Step 4: Factor first two and last two terms 5x(x – 2)- 3(x – 2) (x – 2)(5x – 3) Step 5: Factor out common factor Only works when it does not have a GCF!

9. Factor one more time! Example 2: -3x 2 – 10x + 8 Step 1: Multiply a and c Step 2: Factor Step 3: Rewrite expression with new factors Step 4: Factor first two and last two terms Step 5: Factor out common factor

10. Practice Practice!!! Do #10 and #11