1. Section 4.4

2. a) Factor x 2 + 5x - 36 (x + 9)(x – 4) b) Factor 2x 2 – 20x + 18 Hint: factor out a 2 first 2(x-9)(x-1) c) Factor 2x 2 + x – 6 Why doesn’t (x+3)(x-2) work?

3. Note: The c oefficient of x 2 is different from 1. In this case it is 2 First: Multiply 2 and –6: 2 (– 6) = – 12 1 Next: Find factors of – 12 that add up to 1 – 3 and 4

4. 1.Draw a 2 by 2 grid. 2.Write the first term in the upper left-hand corner 3.Write the last term in the lower right-hand corner.

5. – 3 x 4 = – 12 – 3 + 4 = 1 1.Take the two numbers –3 and 4, and put them, complete with signs and variables, in the diagonal corners, like this: It does not matter which way you do the diagonal entries! Find factors of – 12 that add up to 1 –3 x 4 x

6. 1.Then factor like this: Factor Top RowFactor Bottom Row From Left ColumnFrom Right Column

7. Note: The signs for the bottom row entry and the right column entry come from the closest term that you are factoring from. DO NOT FORGET THE SIGNS!! + + Now that we have factored our box we can read off our answer:

8. a) 2x 2 – 5x – 12 a) 9x 2 + 6x – 24 (can you find a way to make this problem easier?)

9. Finally, you can check your work by multiplying back to get the original answer. Look for factors of 48 that add up to –19 – 16 and – 3