SOLUTION: factor the following m^2+3m-28

Question 117557: factor the following
m^2+3m-28
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 -28 respectively.

Now multiply the first coefficient 1 and the last coefficient -28 to get -28. Now what two numbers multiply to -28 and add to the middle coefficient 3? Let's list all of the factors of -28:

Factors of -28:
1,2,4,7,14,28

-1,-2,-4,-7,-14,-28 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -28
(1)*(-28)
(2)*(-14)
(4)*(-7)
(-1)*(28)
(-2)*(14)
(-4)*(7)

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	-28	1+(-28)=-27
2	-14	2+(-14)=-12
4	-7	4+(-7)=-3
-1	28	-1+28=27
-2	14	-2+14=12
-4	7	-4+7=3

From this list we can see that -4 and 7 add up to 3 and multiply to -28

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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