Factors of 3m⁵-48m are
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3m^5-48m
3m(m^4-16)
3m((m^2)^2-(4)^2)
3m(m^2+4)(m^2-4)
3m(m^2+4)((m)^2-(2)^2)
3m(m^2+4)(m+2)(m-2)
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