3x² + 32x + 48

There is no common factor.  So we will try to factor it
using the ac-method. 

3x² + 32x + 48

Multiply the 3 by the 48.  Get 144

Write down all the ways to have two positive integers
which have product 144, starting with 144*1

144*1
 72*2
 48*3
 36*4
 24*6
 18*8
 16*9
 12*12

Since the last sign in 3x² + 32x + 48 is +, ADD them,
and place the SUM out beside that:

144*1    144+1=145 
 72*2     72+2=74 
 48*3     48+3=51
 36*4     36+4=40
 24*6     24+6=30
 18*8     18+8=26
 16*9     16+9=25
12*12    12+12=24 

Now we look to see if we can find in that list of
sums the coefficient of the middle term in 3x² + 32x + 48

We do not find 32 in that list.  So we cannot continue
with the "ac" method.  So we must stop here and write 

"This trinomial is prime".

There is a lesson on the "ac" method of factoring at this site:

http://www.algebra.com/my/change_this_name32371.lesson?content_action=show_dev 

Edwin