For the above question I get the factorization part but, I do not understand how did greg equate
(t-4)t(t+1) as (t-1)t(t+1) stating in “in terms of multiplicity”.
It has nothing to do with multiplicity, if that’s what’s confusing you. Greg might’ve just used the wrong vocab by accident.
t - 4 \equiv t -1 \pmod 3 is essentially what Greg is getting at.
More simply put, t - 4 leaves the same remainder as t - 1 when divided by 3. As such, in the “remainder after dividing by 3” world, we concede that this holds:
t(t - 4)(t + 1) = t(t-1)(t + 1)
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