2 problems

Univariate factorization conjecture. Such polynomials satisfy the equation if and only if there exist $A,B\in\mathbb{H}[u]$ and $D\in\mathbb{R}[u]$ such that

Let $\mathbb{R}_{22}$ be the real polynomials in commuting variables $u,v$ of degree at most two in each variable, and let $\mathbb{H}_{11}$ be the corresponding quaternionic polyn…