from Wolfram Decker:

f = 15 x^2 + x - 2

f mod 7 = x^2 + x - 2
factors : x+6, x+2

lifting mod 7^2: 15x+6, x+16
multiply by k(t) = 15 mod 7^2:
	-20x-8, 15x-5

Now divide f by these factors.  
If remainder is zero, take 
principal part: 5x+2, 3x-1
