SOLUTION: Factor the trinomial: 2n^2 - 7n - 4

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Question 416125: Factor the trinomial: 2n^2 - 7n - 4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 2n%5E2-7n-4, we can see that the first coefficient is 2, the second coefficient is -7, and the last term is -4.


Now multiply the first coefficient 2 by the last term -4 to get %282%29%28-4%29=-8.


Now the question is: what two whole numbers multiply to -8 (the previous product) and add to the second coefficient -7?


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 -7:


First NumberSecond NumberSum
1-81+(-8)=-7
2-42+(-4)=-2
-18-1+8=7
-24-2+4=2



From the table, we can see that the two numbers 1 and -8 add to -7 (the middle coefficient).


So the two numbers 1 and -8 both multiply to -8 and add to -7


Now replace the middle term -7n with n-8n. Remember, 1 and -8 add to -7. So this shows us that n-8n=-7n.


2n%5E2%2Bhighlight%28n-8n%29-4 Replace the second term -7n with n-8n.


%282n%5E2%2Bn%29%2B%28-8n-4%29 Group the terms into two pairs.


n%282n%2B1%29%2B%28-8n-4%29 Factor out the GCF n from the first group.


n%282n%2B1%29-4%282n%2B1%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.


%28n-4%29%282n%2B1%29 Combine like terms. Or factor out the common term 2n%2B1


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Answer:


So 2n%5E2-7n-4 factors to %28n-4%29%282n%2B1%29.


In other words, 2n%5E2-7n-4=%28n-4%29%282n%2B1%29.


Note: you can check the answer by expanding %28n-4%29%282n%2B1%29 to get 2n%5E2-7n-4 or by graphing the original expression and the answer (the two graphs should be identical).


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Jim