Which polynomial function has a leading coefficient of 2, root –5 with multiplicity 3, and root 12 with multiplicity 1?

A root r gives a factor of (x − r), repeated according to its multiplicity. Root −5 with multiplicity 3 gives (x + 5)³, and root 12 with multiplicity 1 gives (x − 12). Multiplying these factors by the leading coefficient 2 gives 2(x + 5)³(x − 12), which is choice B.

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