I am seeking a common "simple" expression (preferably/presumably a sum of products of linear factors, or sum of products of low-degree factors) uniting the three polynomials (parameterized by y = 1/2, 1 and 2) below. The common expression will be of fourth-degree in k and of arbitrary degree (probably between 3 and 6) in y.

For y = 1/2 (the real case), the polynomial is

-(15/4) (294 + 413 k + 213 k^2 + 48 k^3 + 4 k^4) = -(15/4) (2 + k) (3 + k) (7 + 2 k)^2.

For y = 1 (the complex case), the polynomial is

-24 (990 + 873 k + 280 k^2 + 39 k^3 + 2 k^4) = -24 (3 + k) (5 + k) (6 + k) (11 + 2 k).

For y = 2 (the quaternionic case), the polynomial (NOT now the product of linear factors) is

-60 (13134 + 6925 k + 1291 k^2 + 103 k^3 + 3 k^4) =

-60 (11 + k) (1194 + k (521 + k (70 + 3 k))).

A common expression for y = 1/2 and 1 is

-4 y (1 + y) (2 + y) (1 + k + 2 y) (1 + k + 4 y) (1 + k + 5 y) (3 + 2 k + 8 y),

but not for y = 2.

This question has pertinence to random matrix theory and quantum information topics (cf. http://arxiv.org/abs/1109.2560).