Harristotelian Logic

Thinking about the latest failed idea, it seems to me that the correct answer may be simpler than I thought but kind of weird.

Still with

175x^2 - 15x + 2 = 2(f(x) + 1)*(g(x) + 1)

in an integral domain, it may be true that if

a_1(x) = ((7x-1) +/- sqrt((7x-1)^2 - 4(49x^2 - 14x))/2

and

2f(x) = 5a_1(x) + 5

then f(x) = g(x), so you have that

f(x) = sqrt((175x^2 - 15x + 2)/2) - 1

and if that is true then f(x) is an algebraic integer factor of a_1(x).

If not, then hey, another weird idea wrong, but I think it should be correct, but it still seems weird.

Wacky, but I think it's right.