SOLUTION: Use the ac test to determine if the following trinomial can be factored. If it can be factored, find the values of m and n. 3x^2 + 11x – 4

Different books and different teachers use slightly different
terminology, so I'm not sure what you mean by "m and n".  However
I'll take you through the "ac" method and tell you what part I 
think your teacher means by "m and n".  But you should ask to make
sure.

3x² + 11x - 4

1. Multiply the 3 by the 4, get 12.

2. Notice the sign of the last term is -, so we think "DIFFERENCE".
(If the sign of the last term had been +, we would think "SUM")

3. Think of two positive integers which have product 12 and
DIFFERENCE 11, the coefficient (in absolute value) of the middle term.

It doesn't take long to see that two such positive integers are 
12 and 1.  That's because 12 TIMES 1 is 12 and 12 MINUS 1 is 11.

4. Now use 12 and 1 to rewrite the 11 as (12 - 1)

3x² + (12 - 1)x - 4

5. Remove the parentheses by distributing

3x² + 12x - 1x - 4

[I think your teacher calls m = 12 and n = -1, the coefficients
of x above, but be sure to ask him/her.]

6. Factor by grouping. That is:

a. Factor the first two terms by taking
out 3x.

b. Factor the last two terms by taking out -1

3x(x + 4) - 1(x + 4)

c. Now notice that (x + 4) is contained in both expressions:

3x(x + 4) - 1(x + 4)

d. So factor out the whole (x + 4) leaving 3x when factoring
it out of the left expression, and leaving -1 when factoring
(x + 4) out on the right expression.

(x + 4)(3x - 1)

That's it!

Edwin