SOLUTION: Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions: 2mn - m + 7n - ___

Algebra ->  Expressions-with-variables -> SOLUTION: Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions: 2mn - m + 7n - ___      Log On


   



Question 1209131: Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions:
2mn - m + 7n - ___

Answer by mccravyedwin(408) About Me  (Show Source):
You can put this solution on YOUR website!

2mn - m + 7n - ___

Let's try to factor it, thinking of "FOIL":

%28%22__%22+%2B-+%22__%22%29%28%22__%22+%2B-+%22__%22%29

Let's try 2m and n for the "Firsts"

%282m+%2B-+%22__%22%29%28%22n%22+%2B-+%22__%22%29

Then to get the 7n for the "Inners" we have to put a +7 in the right of the first parentheses.

%282m+%2B7%29%28%22n%22+%2B-+%22__%22%29

Finally to get the -m for the "LASTS" we must put -expr%281%2F2%29 in the remaining blank.

%282m+%2B7%29%28n+-+expr%281%2F2%29%29

So when you FOIL that out you get

2mn-m%2B7n-expr%287%2F2%29

So the term we have to add is the "OUTERS" -expr%287%2F2%29.

[You already had a - sign, so what we'd put in the blank would be expr%287%2F2%29. 

Edwin