Answer
False
Work Step by Step
We determine the Greatest Common Factor (GCF) and factor it out:
$$6y^6-19y^5+10y^4=y^4(6y^2-19y+10).$$
We notice that we can continue factorization of the remaining trinomial:
$$y^4(6y^2-19y+10)=y^4(3y-2)(2y-5).$$
Therefore the given statement is FALSE.
We change it in order to make it true:
Once a GCF is factored from a polynomial, the remaining polynomial factor is SOMETIMES prime.