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

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Question 117557: factor the following
m^2+3m-28
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at m%5E2%2B3m-28 we can see that the first term is m%5E2 and the last term is -28 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 NumberSecond NumberSum
1-281+(-28)=-27
2-142+(-14)=-12
4-74+(-7)=-3
-128-1+28=27
-214-2+14=12
-47-4+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 m%5E2%2B3m-28, replace 3m with -4m%2B7m (notice -4m%2B7m adds up to 3m. So it is equivalent to 3m)

m%5E2%2Bhighlight%28-4m%2B7m%29%2B-28


Now let's factor m%5E2-4m%2B7m-28 by grouping:


%28m%5E2-4m%29%2B%287m-28%29 Group like terms


m%28m-4%29%2B7%28m-4%29 Factor out the GCF of m out of the first group. Factor out the GCF of 7 out of the second group


%28m%2B7%29%28m-4%29 Since we have a common term of m-4, we can combine like terms

So m%5E2-4m%2B7m-28 factors to %28m%2B7%29%28m-4%29


So this also means that m%5E2%2B3m-28 factors to %28m%2B7%29%28m-4%29 (since m%5E2%2B3m-28 is equivalent to m%5E2-4m%2B7m-28)

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Answer:

So m%5E2%2B3m-28 factors to %28m%2B7%29%28m-4%29