Which of the following is a polynomial function in factored form with zeros at 0, –3, and 4? a. f(x) = x^3 + x^2 – 12x b. f(x) = x(x – 3)(x + 4) c. f(x) = x^3 – x^2 – 12x d. f(x) = x(x + 3)(x – 4)

The answer is D.

Explanation:
You can find the zeroes of a polynomial function in factored form by setting each factor equal to zero and solve for .

The polynomial function of answer A is not even factored, so we can rule that one out.

Lets set each one of the factors of answer B equal to zero, solve for  and see what happens:
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As you can see, our zeroes are 0,3, and -4, so this is not the correct answer either.

The polynomial function of answer C is not even factored, so we can rule that one out as well.

Lets apply what we just learned to the factored polynomial of answer D:
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This time our zeroes are, 0, -3, and 4; therefore we can conclude that D is the correct answer.