Rademacher polynomial linear-factor conjecture

Let $g_{\pm1,d}(x)=x^d+a_{d-1}x^{d-1}+\dots+a_0$ be a monic polynomial of odd positive degree $d$, where each $a_i$ is independently $+1$ or $-1$ with probability $\frac{1}{2}$. Rademacher linear-factor conjecture. The probability that $g_{\pm1,d}(x)$ has a linear factor $x+1$ or $x-1$, conditioned on $g_{\pm1,d}(x)$ being reducible, goes to $1$ as $d$ goes to infinity. For odd degree, these are the relevant integer linear factors and provide the asymptotic lower bound discussed in the source; the conjecture predicts that they account for asymptotically all reducibility.