SOLUTION: If one of the factors of the quadratic equation x^2+x-56 is (x+7), then what is the other factor? Answer is: x+8 But how to solve this eqaution?

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Question 915747: If one of the factors of the quadratic equation x^2+x-56 is (x+7), then what is the other factor?
Answer is: x+8
But how to solve this eqaution?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I think you meant to say "x-7" instead of "x+7"

Looking at the expression x%5E2%2Bx-56, we can see that the first coefficient is 1, the second coefficient is 1, and the last term is -56.


Now multiply the first coefficient 1 by the last term -56 to get %281%29%28-56%29=-56.


Now the question is: what two whole numbers multiply to -56 (the previous product) and add to the second coefficient 1?


To find these two numbers, we need to list all of the factors of -56 (the previous product).


Factors of -56:
1,2,4,7,8,14,28,56
-1,-2,-4,-7,-8,-14,-28,-56


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


These factors pair up and multiply to -56.
1*(-56) = -56
2*(-28) = -56
4*(-14) = -56
7*(-8) = -56
(-1)*(56) = -56
(-2)*(28) = -56
(-4)*(14) = -56
(-7)*(8) = -56

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


First NumberSecond NumberSum
1-561+(-56)=-55
2-282+(-28)=-26
4-144+(-14)=-10
7-87+(-8)=-1
-156-1+56=55
-228-2+28=26
-414-4+14=10
-78-7+8=1



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


So the two numbers -7 and 8 both multiply to -56 and add to 1


Now replace the middle term 1x with -7x%2B8x. Remember, -7 and 8 add to 1. So this shows us that -7x%2B8x=1x.


x%5E2%2Bhighlight%28-7x%2B8x%29-56 Replace the second term 1x with -7x%2B8x.


%28x%5E2-7x%29%2B%288x-56%29 Group the terms into two pairs.


x%28x-7%29%2B%288x-56%29 Factor out the GCF x from the first group.


x%28x-7%29%2B8%28x-7%29 Factor out 8 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%2B8%29%28x-7%29 Combine like terms. Or factor out the common term x-7


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Answer:


So x%5E2%2Bx-56 factors to %28x%2B8%29%28x-7%29.


In other words, x%5E2%2Bx-56=%28x%2B8%29%28x-7%29.


Note: you can check the answer by expanding %28x%2B8%29%28x-7%29 to get x%5E2%2Bx-56 or by graphing the original expression and the answer (the two graphs should be identical).


Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim