The square-free approximation conjecture for integer polynomials

Let $f\in\mathbb{Z}[x]$ be a polynomial of degree $d$. A polynomial is square-free if it has no repeated irreducible factor over the rational numbers. Its length is

$$L(f)=\sum_{i=0}^{d}|a_i|$$

when $f(x)=\sum_{i=0}^{d}a_i x^i$.

Square-free approximation conjecture. For any $f\in\mathbb{Z}[x]$ of degree $d$, there is a square-free polynomial $g\in\mathbb{Z}[x]$ of degree at most $d$ satisfying

$$L(f-g)\leq 2.$$

This is a square-free variant of Turán's problem on approximating integer polynomials by irreducible polynomials. The conjecture asks for a uniform bound of $2$ while preserving an upper bound on the degree; its status is not resolved in the supplied source.