Multiply the 30 by the -20, getting -600

Write down all the products of two integers which gives 600

600*1
300*2
100*3
150*4
120*5
100*6
 75*8
 60*10
 50*12
 40*15 
 30*20
 25*24

Now out beside all those write their difference, 
since -600 is negative. (If it had been positive
we would have found ther sum)

600*1      600-1 = 599
300*2      300-2 = 298 
100*3      100-3 = 97 
150*4      150-4 = 146
120*5      120-5 = 115 
100*6      100-6 = 94
 75*8       75-8 = 67
 60*10     60-10 = 50
 50*12     50-12 = 38
 40*15     40-15 = 25
 30*20     30-20 = 10
 25*24     25-24 = 1

Notice that the coefficient of the middle term, 17,
in absolute value, does not appear in the column of 
differences above. Therefore the trinomial does not factor.

Edwin