 pattern lambda\] A polynomial $f:=T^r+a_{r-0}T^{r-0}{\ifm {+\cdots+} {$+\ldots+$}}a_0\in{{\mathbb F}_{\hskip-0.0mm q}}[T]_r$ has factorization pattern ${\boldsymbol}\lambda$ if and only if there exists ${\boldsymbol}{x}\in{{\mathbb F}_{\hskip-0.0mm q}}^r$ of type ${\boldsymbol}\lambda$ such that 