SOLUTION: trial factoring or reverse foil x^2+8x-20

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Question 299535: trial factoring or reverse foil
x^2+8x-20
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression x%5E2%2B8x-20, we can see that the first coefficient is 1, the second coefficient is 8, and the last term is -20.


Now multiply the first coefficient 1 by the last term -20 to get %281%29%28-20%29=-20.


Now the question is: what two whole numbers multiply to -20 (the previous product) and add to the second coefficient 8?


To find these two numbers, we need to list all of the factors of -20 (the previous product).


Factors of -20:
1,2,4,5,10,20
-1,-2,-4,-5,-10,-20


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


These factors pair up and multiply to -20.
1*(-20) = -20
2*(-10) = -20
4*(-5) = -20
(-1)*(20) = -20
(-2)*(10) = -20
(-4)*(5) = -20

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 8:


First NumberSecond NumberSum
1-201+(-20)=-19
2-102+(-10)=-8
4-54+(-5)=-1
-120-1+20=19
-210-2+10=8
-45-4+5=1



From the table, we can see that the two numbers -2 and 10 add to 8 (the middle coefficient).


So the two numbers -2 and 10 both multiply to -20 and add to 8


Now replace the middle term 8x with -2x%2B10x. Remember, -2 and 10 add to 8. So this shows us that -2x%2B10x=8x.


x%5E2%2Bhighlight%28-2x%2B10x%29-20 Replace the second term 8x with -2x%2B10x.


%28x%5E2-2x%29%2B%2810x-20%29 Group the terms into two pairs.


x%28x-2%29%2B%2810x-20%29 Factor out the GCF x from the first group.


x%28x-2%29%2B10%28x-2%29 Factor out 10 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%2B10%29%28x-2%29 Combine like terms. Or factor out the common term x-2


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Answer:


So x%5E2%2B8x-20 factors to %28x%2B10%29%28x-2%29.


In other words, x%5E2%2B8x-20=%28x%2B10%29%28x-2%29.


Note: you can check the answer by expanding %28x%2B10%29%28x-2%29 to get x%5E2%2B8x-20 or by graphing the original expression and the answer (the two graphs should be identical).