SOLUTION: trial and error answer for 2x^2-5x-7

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Question 590924: trial and error answer for 2x^2-5x-7
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Looking at the expression 2x%5E2-5x-7, we can see that the first coefficient is 2, the second coefficient is -5, and the last term is -7.


Now multiply the first coefficient 2 by the last term -7 to get %282%29%28-7%29=-14.


Now the question is: what two whole numbers multiply to -14 (the previous product) and add to the second coefficient -5?


To find these two numbers, we need to list all of the factors of -14 (the previous product).


Factors of -14:
1,2,7,14
-1,-2,-7,-14


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


These factors pair up and multiply to -14.
1*(-14) = -14
2*(-7) = -14
(-1)*(14) = -14
(-2)*(7) = -14

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -5:


First NumberSecond NumberSum
1-141+(-14)=-13
2-72+(-7)=-5
-114-1+14=13
-27-2+7=5



From the table, we can see that the two numbers 2 and -7 add to -5 (the middle coefficient).


So the two numbers 2 and -7 both multiply to -14 and add to -5


Now replace the middle term -5x with 2x-7x. Remember, 2 and -7 add to -5. So this shows us that 2x-7x=-5x.


2x%5E2%2Bhighlight%282x-7x%29-7 Replace the second term -5x with 2x-7x.


%282x%5E2%2B2x%29%2B%28-7x-7%29 Group the terms into two pairs.


2x%28x%2B1%29%2B%28-7x-7%29 Factor out the GCF 2x from the first group.


2x%28x%2B1%29-7%28x%2B1%29 Factor out 7 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-7%29%28x%2B1%29 Combine like terms. Or factor out the common term x%2B1


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Answer:


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


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


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

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