Final answer:
The polynomial -27m⁶ + 6m³ is factored by first finding the greatest common factor, which is -3m³. After factoring out -3m³, the complete factored form is -3m³(9m³ - 2).
Step-by-step explanation:
The student has asked to find the complete factored form of the polynomial -27m⁶ + 6m³. To factor this polynomial, we first look for the greatest common factor (GCF) between the two terms, which in this case is 6m³. However, because our leading coefficient is negative, we should use -3m³ as our GCF. Factor out the GCF:
Upon doing this, notice that we have factored out not only the greatest common factor of the m terms, m³, but also we've accounted for the coefficient correctly by dividing both terms by -3m³. The correct complete factored form is -3m³(9m³ - 2), which corresponds to option B.