I am to factor 3y^2+10y+7, the trinomial using the ac method. Can someone
help me answer this question.

Step by Step method for factoring a trinomial

Ax2 + Bx + C (any letter may be where x is here)

Step 1: If a greatest common factor can be factored out, do
that first, then apply the following to the resulting
trinomial in parentheses.

Step 2.  Multiply together AC and list the factors of AC.

Step 3.  Find a pair that adds to B.  If you cannot find such
a pair then the trinomial does not factor.

Step 4.  Rewrite the middle term as a sum of terms whose
coefficients are the chosen pair.

Step 5.  Factor by grouping. 

To factor  

        3y2 + 10y + 7

AC = (3)(7) = 21

the factor pairs are 

        {1,21} and  {3,7}         

We see that  

        3 + 7  =  10   hence we choose the pair {3,7}

We write  
 
        3y2 + 10y + 7
        
as
        3y2 + 3y + 7y + 7

Then we group the first two terms and the last two terms.

       (3y2 + 3y) + (7y + 7)

Factor 3y out of the first parentheses and 7 out of the second.

       3y(y + 1) + 7(y + 1)  

Factor out the common factor (y + 1)

       (y + 1)(3y + 7)

Edwin
AnlytcPhil@aol.com