In order to factor  , first multiply the leading coefficient 1 and the last term -88 to get -88. Now we need to ask ourselves: What two numbers multiply to -88 and add to -3? Lets find out by listing all of the possible factors of -88
Factors:
1,2,4,8,11,22,44,88,
-1,-2,-4,-8,-11,-22,-44,-88, List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to -88.
(-1)*(88)=-88
(-2)*(44)=-88
(-4)*(22)=-88
(-8)*(11)=-88
Now which of these pairs add to -3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -3
| First Number | | | Second Number | | | Sum | | 1 | | | -88 | || | 1+(-88)=-87 | | 2 | | | -44 | || | 2+(-44)=-42 | | 4 | | | -22 | || | 4+(-22)=-18 | | 8 | | | -11 | || | 8+(-11)=-3 | | -1 | | | 88 | || | (-1)+88=87 | | -2 | | | 44 | || | (-2)+44=42 | | -4 | | | 22 | || | (-4)+22=18 | | -8 | | | 11 | || | (-8)+11=3 |
We can see from the table that 8 and -11 add to -3. So the two numbers that multiply to -88 and add to -3 are: 8 and -11
So the original quadratic
breaks down to this (just replace  with the two numbers that multiply to -88 and add to -3, which are: 8 and -11)
 Replace with 
Group the first two terms together and the last two terms together like this:
Factor a 1b out of the first group and factor a -11 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. |
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