SOLUTION: Use the ac test to determine which trinomials can be factored. Find the values of m and n for each trinomial that can be factored. x^2-3x+7

Click here to see ALL problems on Polynomials-and-rational-expressions

Question 117377: Use the ac test to determine which trinomials can be factored. Find the values of m and n for each trinomial that can be factored.
x^2-3x+7
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 7 respectively.

Now multiply the first coefficient 1 and the last coefficient 7 to get 7. Now what two numbers multiply to 7 and add to the middle coefficient -3? Let's list all of the factors of 7:

Factors of 7:
1,7

-1,-7 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 7
1*7
(-1)*(-7)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -3

First Number Second Number Sum
1 7 1+7=8
-1 -7 -1+(-7)=-8

None of these pairs of factors add to -3. So the expression cannot be factored