SOLUTION: factor 2m^2-9m+4

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Question 787996: factor 2m^2-9m+4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 2m%5E2-9m%2B4, we can see that the first coefficient is 2, the second coefficient is -9, and the last term is 4.


Now multiply the first coefficient 2 by the last term 4 to get %282%29%284%29=8.


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


To find these two numbers, we need to list all of the factors of 8 (the previous product).


Factors of 8:
1,2,4,8
-1,-2,-4,-8


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


These factors pair up and multiply to 8.
1*8 = 8
2*4 = 8
(-1)*(-8) = 8
(-2)*(-4) = 8

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -9:


First NumberSecond NumberSum
181+8=9
242+4=6
-1-8-1+(-8)=-9
-2-4-2+(-4)=-6



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


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


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


2m%5E2%2Bhighlight%28-m-8m%29%2B4 Replace the second term -9m with -m-8m.


%282m%5E2-m%29%2B%28-8m%2B4%29 Group the terms into two pairs.


m%282m-1%29%2B%28-8m%2B4%29 Factor out the GCF m from the first group.


m%282m-1%29-4%282m-1%29 Factor out 4 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-4%29%282m-1%29 Combine like terms. Or factor out the common term 2m-1


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Answer:


So 2m%5E2-9m%2B4 factors to %28m-4%29%282m-1%29.


In other words, 2m%5E2-9m%2B4=%28m-4%29%282m-1%29.


Note: you can check the answer by expanding %28m-4%29%282m-1%29 to get 2m%5E2-9m%2B4 or by graphing the original expression and the answer (the two graphs should be identical).