SOLUTION: Factor 4m^2-8m+3

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Question 168692: Factor
4m^2-8m+3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 4m%5E2-8m%2B3, we can see that the first coefficient is 4, the second coefficient is -8, and the last term is 3.


Now multiply the first coefficient 4 by the last term 3 to get %284%29%283%29=12.


Now the question is: what two whole numbers multiply to 12 (the previous product) and add to the second coefficient -8?


To find these two numbers, we need to list all of the factors of 12 (the previous product).


Factors of 12:
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12


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


These factors pair up and multiply to 12.
1*12
2*6
3*4
(-1)*(-12)
(-2)*(-6)
(-3)*(-4)

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


First NumberSecond NumberSum
1121+12=13
262+6=8
343+4=7
-1-12-1+(-12)=-13
-2-6-2+(-6)=-8
-3-4-3+(-4)=-7



From the table, we can see that the two numbers -2 and -6 add to -8 (the middle coefficient).


So the two numbers -2 and -6 both multiply to 12 and add to -8


Now replace the middle term -8m with -2m-6m. Remember, -2 and -6 add to -8. So this shows us that -2m-6m=-8m.


4m%5E2%2Bhighlight%28-2m-6m%29%2B3 Replace the second term -8m with -2m-6m.


%284m%5E2-2m%29%2B%28-6m%2B3%29 Group the terms into two pairs.


2m%282m-1%29%2B%28-6m%2B3%29 Factor out the GCF 2m from the first group.


2m%282m-1%29-3%282m-1%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.


%282m-3%29%282m-1%29 Combine like terms. Or factor out the common term 2m-1

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Answer:


So 4m%5E2-8m%2B3 factors to %282m-3%29%282m-1%29.


Note: you can check the answer by FOILing %282m-3%29%282m-1%29 to get 4m%5E2-8m%2B3 or by graphing the original expression and the answer (the two graphs should be identical).