The factor function computes the factorization of a multivariate polynomial with integer, rational, (complex) numeric, or algebraic number coefficients.

The factor(M) command computes the element-wise factorization of M.  The result, R, is formed as R[i,j] = factor(M[i,j]).

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$M≔\mathrm{Matrix}\left(2\,3\,'\mathrm{fill}'=ax+ya\right)\:$

$\mathrm{factor}\left(M\right)$

$\left[\begin{array}{ccc}a\left(x+y\right)& a\left(x+y\right)& a\left(x+y\right)\\ a\left(x+y\right)& a\left(x+y\right)& a\left(x+y\right)\end{array}\right]$