SOLUTION: 8x^2-4x-4

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Question 588452: 8x^2-4x-4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor this.



8x%5E2-4x-4 Start with the given expression.


4%282x%5E2-x-1%29 Factor out the GCF 4.


Now let's try to factor the inner expression 2x%5E2-x-1


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Looking at the expression 2x%5E2-x-1, we can see that the first coefficient is 2, the second coefficient is -1, and the last term is -1.


Now multiply the first coefficient 2 by the last term -1 to get %282%29%28-1%29=-2.


Now the question is: what two whole numbers multiply to -2 (the previous product) and add to the second coefficient -1?


To find these two numbers, we need to list all of the factors of -2 (the previous product).


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


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


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

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -1:


First NumberSecond NumberSum
1-21+(-2)=-1
-12-1+2=1



From the table, we can see that the two numbers 1 and -2 add to -1 (the middle coefficient).


So the two numbers 1 and -2 both multiply to -2 and add to -1


Now replace the middle term -1x with x-2x. Remember, 1 and -2 add to -1. So this shows us that x-2x=-1x.


2x%5E2%2Bhighlight%28x-2x%29-1 Replace the second term -1x with x-2x.


%282x%5E2%2Bx%29%2B%28-2x-1%29 Group the terms into two pairs.


x%282x%2B1%29%2B%28-2x-1%29 Factor out the GCF x from the first group.


x%282x%2B1%29-1%282x%2B1%29 Factor out 1 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.


%28x-1%29%282x%2B1%29 Combine like terms. Or factor out the common term 2x%2B1


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So 4%282x%5E2-x-1%29 then factors further to 4%28x-1%29%282x%2B1%29


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Answer:


So 8x%5E2-4x-4 completely factors to 4%28x-1%29%282x%2B1%29.


In other words, 8x%5E2-4x-4=4%28x-1%29%282x%2B1%29.


Note: you can check the answer by expanding 4%28x-1%29%282x%2B1%29 to get 8x%5E2-4x-4 or by graphing the original expression and the answer (the two graphs should be identical).

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