SOLUTION: factor completely: x^2+9x=8

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Question 101318: factor completely:
x^2+9x=8
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation

Subtract 8 from both sides


Now let's factor


Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .



Now multiply the first coefficient by the last term to get .



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



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



Factors of :

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 .

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 :



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 there are no pairs of numbers which add to . So cannot be factored.



===============================================================





Answer:



So doesn't factor at all (over the rational numbers).



So is prime.
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