1. X-Puzzles  This is usually introduced in Pre-algebra (7th grade).  It’s a simple pattern that is discovered, but tends to not be taught.

2. X-Puzzles Using the pattern in puzzles A and B, complete puzzles C, D and E. Did you get? 10 7 1410 2124 Pretty easy, right?

3. X-Puzzles Try these!

4. X-Puzzles Look at these puzzles when different parts are missing

5. X-Puzzles - continued See if you can solve these harder ones.

6. X puzzles – WHY WERE WE DOING THIS???  When we did the area models  They always were set up for us  We knew what the coefficients of x were  We DON’T know how to fill in the blanks if they are missing  The X-Puzzles  Give you the coefficients that go in the missing spaces.  Allow you to have a visual for finding unknown values.  Are pretty straight forward once you get the hang of them.

7. Here’s an example of using the X-Puzzle Given: x 2 + 13x +36 36 9 13 4 x2x2 369x 4x x 9 x4 Answer: x 2 + 13x +36 = (x + 9)(x + 4) Same numbers that were in the x-puzzle!

8. You try one!  Given: x 2 + 5x + 6 6 5 23 2x 3x x2x2 6 x 2 x3 Answer: x 2 + 5x + 6 = (x + 2)(x + 3)

9. One more…  Given: x 2 - 10x - 24 Answer: x 2 - 10x – 24=(x + 2)(x - 12) -24 -10 -122 -12x 2xx2x2 -24 x -12 2x

10. It even works with the difference of 2 squares (“b” term is missing)!  Given: x 2 -9 -9 0 -33 -3x 3x x2x2 -9 x -3 x3 Answer: x 2 - 9 = (x - 3)(x + 3)

11. It also works if the constant term is missing!  Given: 4x 2 -8x 0 -8x 0 0 4x 2 0 x -2 4x0 Answer: 4x(x - 2) Since there is a column of zeros, we can get rid of it

12. Now, it’s time to see you do it on your own  Set up the x puzzles and the area models to factor the following polynomials. 1) x 2 + 3x + 2 2) x 2 + 5x + 6 3) x 2 - 7x + 10 4) x 2 - 8x - 9

13. Now, there are times when you’re given a coefficient in front of the x 2.  Don’t panic, you still have all the tools necessary to solve these, we just need to modify our x-puzzles.  Example: 2x 2 + 3x + 1  HOWEVER, you’ll need to look at the coefficient on the 2x 2 2x 2 1 1 x 2x 2*?? 3 Thus, 2x 2 +3x+1=(2x+1)(x+1) 2*11 2x x 1 1

14. Let’s look at a harder one.  3x 2 + 11x + 10  Still, you’ll need to look at the coefficient on the x 2 3x 2 10 x 3x 3*?? 11 Thus, 3x 2 +11x+10=(3x+5)(x+2) 3*25 6x 5x 2 5

15. Here is the modification that is much easier.  3x 2 + 11x + 10  ALL YOU NEED TO DO, IS MULTIPLY YOUR OUTSIDE NUMBERS FIRST. (3x10) This goes on your x-puzzle where the product normally goes. 3x 2 10 30 x 3x ?? 11 Thus, 3x 2 +11x+10=(3x+5)(x+2) 56 6x 5x 2 5

16. One more, but the steps are broken down.  2x 2 + 9x + 10 2x 2 10 2x x Step 1: Draw the area model and x-puzzle Step 2: Fill in what information you can in both the area model and x-puzzle. 20 9 Step 3: Multiply the outside numbers. In this case, 2 and 10. ?? Step 4: Solve the x-puzzle and put those values into your area model 4x 5x 45 2 5 Step 5: Find the missing pieces and write your final answer. 2x 2 + 9x + 10 = (2x+5)(x+2) 2x10=20

17. Try these three on your own 1) 4x 2 + 4x -3 2) 2x 2 + 7x + 5 3) 8x 2 – 14x -9

18. And that’s the basics to factoring with two visual tools