SOLUTION: 2x^2-4x+2

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Question 168141: 2x^2-4x+2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 2x%5E2-4x%2B2, we can see that the first coefficient is 2, the second coefficient is -4, and the last term is 2.


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


Now the question is: what two whole numbers multiply to 4 (the previous product) and add to the second coefficient -4?


To find these two numbers, we need to list all of the factors of 4 (the previous product).


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


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


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

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -4:


First NumberSecond NumberSum
141+4=5
222+2=4
-1-4-1+(-4)=-5
-2-2-2+(-2)=-4



From the table, we can see that the two numbers -2 and -2 add to -4 (the middle coefficient).


So the two numbers -2 and -2 both multiply to 4 and add to -4


Now replace the middle term -4x with -2x-2x. Remember, -2 and -2 add to -4. So this shows us that -2x-2x=-4x.


2x%5E2%2Bhighlight%28-2x-2x%29%2B2 Replace the second term -4x with -2x-2x.


%282x%5E2-2x%29%2B%28-2x%2B2%29 Group the terms into two pairs.


2x%28x-1%29%2B%28-2x%2B2%29 Factor out the GCF 2x from the first group.


2x%28x-1%29-2%28x-1%29 Factor out 2 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.


%282x-2%29%28x-1%29 Combine like terms. Or factor out the common term x-1

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Answer:


So 2x%5E2-4x%2B2 factors to %282x-2%29%28x-1%29.


Note: you can check the answer by FOILing %282x-2%29%28x-1%29 to get 2x%5E2-4x%2B2 or by graphing the original expression and the answer (the two graphs should be identical).