SOLUTION: Use the ac test to determine which of the following trinomials can be factored. Find the values of m and n for each trinomial that can be factored. x squared - x + 2

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Question 114758: Use the ac test to determine which of the following trinomials can be factored. Find the values of m and n for each trinomial that can be factored.
x squared - x + 2

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
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

-1,-2



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



These factors pair up and multiply to .

1*2 = 2
(-1)*(-2) = 2


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



First NumberSecond NumberSum
121+2=3
-1-2-1+(-2)=-3




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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