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If I wanted to describe a multivariable polynomial that could be factored into linear factors $p(x)=\prod_i \left( a_ix+b_it+c_i\right)$, what should I say?

For example, $x^2-t^2$ would belong but but $x^2-t$ would not.

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I would probably just say "factors into linears" or "is a product of linear polynomials" or the like.

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You could say "it splits completely", although I've only ever heard that used for univariate polynomials.

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