Question 185339
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


{{{12x^2+16x-9x-12}}}


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


{{{12x^2-9x+16x-12}}}



5)


{{{(12x^2-9x)+(16x-12)}}} Group the terms into pairs



{{{3x(4x-3)+(16x-12)}}} Factor out the GCF 3x from the first group



{{{3x(4x-3)+4(4x-3)}}} Factor out the GCF 4 from the second group



Notice how we have the common factor {{{4x-3}}}, we can factor that out to get


{{{(3x+4)(4x-3)}}}



which is the final factorization.


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Answer:



So {{{12x^2+7x-12}}} factors to {{{(3x+4)(4x-3)}}} (note: the order of the factors does NOT matter).



In other words, {{{12x^2+7x-12=(3x+4)(4x-3)}}}



So the entire breakdown looks like this:



{{{(3x+4)(4x-3)=12x^2-9x+16x-12=12x^2+7x-12}}}