read NearestNpoly:
f1 := randpoly([x,y],degree=4,dense);
f2 := randpoly([x,y],degree=5,dense);
f := expand(f1*f2)/99;
F := evalf(f, 3);

NF := NearestNpoly(F, 20);

res := TrivialFactoring(NF, 20);

Digits := 15:
	Distance(expand(res),NF):
	"Distance res to NF is:", evalf(%,6);
Digits := 10:
"Distance NF to F is:", Distance(NF, F);
"Distance f to F is:", Distance(f, F);

# Again, we found a reducible polynomial NF, with factorization res,
# that is closer to the input F than f was.