SOLUTION: How do I factor this problem? 3m squared - 8m - 3

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Question 189872: How do I factor this problem?
3m squared - 8m - 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 3m%5E2-8m-3, we can see that the first coefficient is 3, the second coefficient is -8, and the last term is -3.


Now multiply the first coefficient 3 by the last term -3 to get %283%29%28-3%29=-9.


Now the question is: what two whole numbers multiply to -9 (the previous product) and add to the second coefficient -8?


To find these two numbers, we need to list all of the factors of -9 (the previous product).


Factors of -9:
1,3,9
-1,-3,-9


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to -9.
1*(-9)
3*(-3)
(-1)*(9)
(-3)*(3)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -8:


First NumberSecond NumberSum
1-91+(-9)=-8
3-33+(-3)=0
-19-1+9=8
-33-3+3=0



From the table, we can see that the two numbers 1 and -9 add to -8 (the middle coefficient).


So the two numbers 1 and -9 both multiply to -9 and add to -8


Now replace the middle term -8m with m-9m. Remember, 1 and -9 add to -8. So this shows us that m-9m=-8m.


3m%5E2%2Bhighlight%28m-9m%29-3 Replace the second term -8m with m-9m.


%283m%5E2%2Bm%29%2B%28-9m-3%29 Group the terms into two pairs.


m%283m%2B1%29%2B%28-9m-3%29 Factor out the GCF m from the first group.


m%283m%2B1%29-3%283m%2B1%29 Factor out 3 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28m-3%29%283m%2B1%29 Combine like terms. Or factor out the common term 3m%2B1

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Answer:


So 3m%5E2-8m-3 factors to %28m-3%29%283m%2B1%29.


Note: you can check the answer by FOILing %28m-3%29%283m%2B1%29 to get 3m%5E2-8m-3 or by graphing the original expression and the answer (the two graphs should be identical).