SOLUTION: right side completely factor -2x^2+76x+430

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Question 610256: right side completely factor
-2x^2+76x+430
Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-2x%5E2%2B76x%2B430 Start with the given expression.


-2%28x%5E2-38x-215%29 Factor out the GCF -2.


Now let's try to factor the inner expression x%5E2-38x-215


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Looking at the expression x%5E2-38x-215, we can see that the first coefficient is 1, the second coefficient is -38, and the last term is -215.


Now multiply the first coefficient 1 by the last term -215 to get %281%29%28-215%29=-215.


Now the question is: what two whole numbers multiply to -215 (the previous product) and add to the second coefficient -38?


To find these two numbers, we need to list all of the factors of -215 (the previous product).


Factors of -215:
1,5,43,215
-1,-5,-43,-215


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


These factors pair up and multiply to -215.
1*(-215) = -215
5*(-43) = -215
(-1)*(215) = -215
(-5)*(43) = -215

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -38:


First NumberSecond NumberSum
1-2151+(-215)=-214
5-435+(-43)=-38
-1215-1+215=214
-543-5+43=38



From the table, we can see that the two numbers 5 and -43 add to -38 (the middle coefficient).


So the two numbers 5 and -43 both multiply to -215 and add to -38


Now replace the middle term -38x with 5x-43x. Remember, 5 and -43 add to -38. So this shows us that 5x-43x=-38x.


x%5E2%2Bhighlight%285x-43x%29-215 Replace the second term -38x with 5x-43x.


%28x%5E2%2B5x%29%2B%28-43x-215%29 Group the terms into two pairs.


x%28x%2B5%29%2B%28-43x-215%29 Factor out the GCF x from the first group.


x%28x%2B5%29-43%28x%2B5%29 Factor out 43 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-43%29%28x%2B5%29 Combine like terms. Or factor out the common term x%2B5


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So -2%28x%5E2-38x-215%29 then factors further to -2%28x-43%29%28x%2B5%29


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Answer:


So -2x%5E2%2B76x%2B430 completely factors to -2%28x-43%29%28x%2B5%29.


In other words, -2x%5E2%2B76x%2B430=-2%28x-43%29%28x%2B5%29.


Note: you can check the answer by expanding -2%28x-43%29%28x%2B5%29 to get -2x%5E2%2B76x%2B430 or by graphing the original expression and the answer (the two graphs should be identical).


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Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
find factors of -860 which ad up to 76
or better factor out the -2 first and find factors of -215 which add up to -38
-2*(x^2-43x+5x-215)
-2*(x*(x-43) +5*(x-43)
-2 *(x+5)*(x-43)