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

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Question 101318: factor completely:
x^2+9x=8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B9x=8 Start with the given equation

x%5E2%2B9x-8=0 Subtract 8 from both sides


Now let's factor x%5E2%2B9x-8


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


Looking at the expression x%5E2%2B9x-8, we can see that the first coefficient is 1, the second coefficient is 9, and the last term is -8.



Now multiply the first coefficient 1 by the last term -8 to get %281%29%28-8%29=-8.



Now the question is: what two whole numbers multiply to -8 (the previous product) and add to the second coefficient 9?



To find these two numbers, we need to list all of the factors of -8 (the previous product).



Factors of -8:

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 -8.

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 9:



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 9. So x%5E2%2B9x-8 cannot be factored.



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Answer:



So x%5E2%2B9%2Ax-8 doesn't factor at all (over the rational numbers).



So x%5E2%2B9%2Ax-8 is prime.