What are the zeros of the polynomial functionF(x) = x3 - x2 - 6x?A.x = -3, x = 0, and x = 2B.x = -1, x = 0, and x = 6C.x = -2, x = 0, and x = 3D.x = -6, x = 0, and x = 1SUBMITarrow_backPREVIOUS
Question
What are the zeros of the polynomial functionF(x) = x3 - x2 - 6x?A.x = -3, x = 0, and x = 2B.x = -1, x = 0, and x = 6C.x = -2, x = 0, and x = 3D.x = -6, x = 0, and x = 1SUBMITarrow_backPREVIOUS
Solution
To find the zeros of the polynomial function F(x) = x³ - x² - 6x, we need to set the function equal to zero and solve for x.
0 = x³ - x² - 6x
First, we can factor out an x:
0 = x(x² - x - 6)
Then, we can factor the quadratic:
0 = x(x - 3)(x + 2)
Setting each factor equal to zero gives the solutions:
x = 0, x = 3, x = -2
So, the zeros of the function are x = -2, x = 0, and x = 3. Therefore, the correct answer is C. x = -2, x = 0, and x = 3.
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