SOLUTION: could use your help with this we are suppose to fill in the answer.Also if you could explain your steps when possible, you guys are wonderful on here, and thank you so much. This i

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Question 185339: could use your help with this we are suppose to fill in the answer.Also if you could explain your steps when possible, you guys are wonderful on here, and thank you so much. This is a foil question
( )( )= 12x^2 -9x +16x -12 = 12x^2 +7X -12 We are to fill the first part of the answer.

Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
( )( )= 12x^2 -9x +16x -12
Because the sign on the constant (-12) is negative, you know that one term has a plus in it and the other has a minus. You also know that each term has an x in them
(Ax + B)(Cx - D) = 12x^2 -9x +16x -12
You know that AC = 12, -AD = -9, BC=16 and -BD=-12.
There are only a few pairs of integers that yield a product of 12.
They are (1,12) (2,6) (3,4)
When you look at the inner terms you see a 9 and a 16. 9 is 3*3 and 16 is 4*4, so 3 and 4 are good guesses to try first
Try
(4x + 3)(3x - 4)
You can see that you get 3*3 = 9 and 4*(-4)= -16. The signs don't match the given equation. So flip them
(4x -3)(3x +4)
Now you get -9 and 16. so this looks like a winner

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
If you are familiar with the FOIL method, then what you are simply doing here is undoing that method to find the answer.

Now there's a lot going on here (let me know if you need a more detailed explanation), but here's the basic idea:

1) First multiply the first coefficient 12 by the last term -12 to get -144

2) List the factors to -144 (both positive and negative) that multiply to -144. So
-144=-1*144, -144=-2*72, -144=4*36, etc...

3) Now the big question is: what two WHOLE numbers both add to the middle coefficient 7 and multiply to -144?

If you try some numbers out (by guessing or making a table), you'll see that the two numbers are 16 and -9

In other words, 16(-9)=-144 AND 16+(-9)=7

4) Break up the middle term 7x into 16x-9x (take note of the 16 and the -9) to get

Note: you can reorder the terms (to match your book) to get

5)

Group the terms into pairs

Factor out the GCF 3x from the first group

Factor out the GCF 4 from the second group

Notice how we have the common factor , we can factor that out to get

which is the final factorization.

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Answer:

So factors to (note: the order of the factors does NOT matter).

In other words,

So the entire breakdown looks like this: