Rearrange terms in descending order:



Write down all pairs of positive integers which have product 45:

1*45=45
3*15=45
 5*9=45
 


Since the last sign is , out beside those pairs,
write their sum
 
1*45=45   1+45=46
3*15=45   3+15=18
 5*9=45    5+9=15



Look for the red  among them. 

We find it at the pair of factors 3 and 15,
so we write

(x   3)(x   15)

Since the last term of  is
positive, the signs are like and are the
same as the sign of the middle term 
So the factorization is

(x + 3)(x + 15)

Edwin