In order to factor  , first multiply the leading coefficient 3 and the last term -4 to get -12. Now we need to ask ourselves: What two numbers multiply to -12 and add to 4? Lets find out by listing all of the possible factors of -12
Factors:
1,2,3,4,6,12,
-1,-2,-3,-4,-6,-12, List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to -12.
(-1)*(12)=-12
(-2)*(6)=-12
(-3)*(4)=-12
Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4
| First Number | | | Second Number | | | Sum | | 1 | | | -12 | || | 1+(-12)=-11 | | 2 | | | -6 | || | 2+(-6)=-4 | | 3 | | | -4 | || | 3+(-4)=-1 | | -1 | | | 12 | || | (-1)+12=11 | | -2 | | | 6 | || | (-2)+6=4 | | -3 | | | 4 | || | (-3)+4=1 |
We can see from the table that -2 and 6 add to 4. So the two numbers that multiply to -12 and add to 4 are: -2 and 6
So the original quadratic
breaks down to this (just replace  with the two numbers that multiply to -12 and add to 4, which are: -2 and 6)
 Replace with 
Group the first two terms together and the last two terms together like this:
Factor a 1x out of the first group and factor a 2 out of the second group.
Now since we have a common term  we can combine the two terms.
 Combine like terms.
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Answer:
So the quadratic factors to
Notice how foils back to our original problem . This verifies our answer. |
