Question 125882: Factor:
x^2+3x-18
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Looking at  we can see that the first term is  and the last term is  where the coefficients are 1 and -18 respectively.
Now multiply the first coefficient 1 and the last coefficient -18 to get -18. Now what two numbers multiply to -18 and add to the middle coefficient 3? Let's list all of the factors of -18:
Factors of -18:
1,2,3,6,9,18
-1,-2,-3,-6,-9,-18 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -18
(1)*(-18)
(2)*(-9)
(3)*(-6)
(-1)*(18)
(-2)*(9)
(-3)*(6)
note: remember, the product of a negative and a positive number is a negative number
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 | -18 | 1+(-18)=-17 | | 2 | -9 | 2+(-9)=-7 | | 3 | -6 | 3+(-6)=-3 | | -1 | 18 | -1+18=17 | | -2 | 9 | -2+9=7 | | -3 | 6 | -3+6=3 |
From this list we can see that -3 and 6 add up to 3 and multiply to -18
Now looking at the expression , replace  with  (notice adds up to . So it is equivalent to )
Now let's factor  by grouping:
 Group like terms
 Factor out the GCF of  out of the first group. Factor out the GCF of  out of the second group
 Since we have a common term of  , we can combine like terms
So factors to
So this also means that factors to (since is equivalent to )
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Answer:
So  factors to
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