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3 x ( 2 x 3 + x 2 − 4 )

Step-by-step explanation:

Factor  3 x  out of  3 x 3 . 3 x ( x 2 ) − 12 x + 6 x 4

Factor  3 x  out of  − 12 x . 3 x ( x 2 ) + 3 x ( − 4 ) + 6 x 4

Factor  3 x  out of  6 x 4 . 3 x ( x 2 ) + 3 x ( − 4 ) + 3 x ( 2 x 3 )

Factor  3 x  out of  3 x ( x 2 ) + 3 x ( − 4 ) . 3 x ( x 2 − 4 ) + 3 x ( 2 x 3 )

Factor  3 x  out of  3 x ( x 2 − 4 ) + 3 x ( 2 x 3 ) . 3 x ( x 2 − 4 + 2 x 3 )

Reorder terms. 3 x ( 2 x 3 + x 2 − 4 )

so the Greatest common factor of 3x^3 - 12x + 6x4 is 3 x ( 2 x 3 + x 2 − 4 )