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)

1 answer
Question:

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)


Answers

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 [tex]x[/tex].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 [tex]x[/tex] and see what happens:- [tex]x=0[/tex]- [tex]x-3=0[/tex]  [tex]x=3[/tex]- [tex]x+4=0[/tex]  [tex]x=-4[/tex]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:- [tex]x=0[/tex]- [tex]x+3=0[/tex]  [tex]x=-3[/tex]- [tex]x-4=0[/tex]  [tex]x=4[/tex]This time our zeroes are, 0, -3, and 4; therefore we can conclude that D is the correct answer.

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