Section 4.4

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?

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

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.

– 3 x 4 = – 12 – = 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

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

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:

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

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