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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (Show Source):
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Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression x%5E2-x%2B2, we can see that the first coefficient is 1, the second coefficient is -1, and the last term is 2.



Now multiply the first coefficient 1 by the last term 2 to get %281%29%282%29=2.



Now the question is: what two whole numbers multiply to 2 (the previous product) and add to the second coefficient -1?



To find these two numbers, we need to list all of the factors of 2 (the previous product).



Factors of 2:

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 2.

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 -1:



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 -1. So x%5E2-x%2B2 cannot be factored.



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Answer:



So x%5E2-x%2B2 doesn't factor at all (over the rational numbers).



So x%5E2-x%2B2 is prime.