Answer:
D. f(x) = -6x^3 -5x^2 +21x
Step-by-step explanation:
The given zeros mean the function has factors ...
(x -(-7/3))(x -3/2)(x -0)
Multiplying by 6, we can write this as ...
(3x +7)(2x -3)(x) = 6x^3 +5x^2 -21x
And multiplying by -1 gives ...
-6x^3 -5x^2 +21x . . . . . matches choice D
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Additional comment
The product of factors will be zero when f(x) = 0. This means we can multiply or divide by any convenient factor and the product will remain zero. Effectively, we have multiplied our original factorization by -6 to make the expression match one of the given forms. When we write this final expression as the function f(x), it remains true that the given zeros are zeros (x-intercepts) of f(x).
