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Find the zeros of the polynomial function:
f(x) = 9x^3 - 27x^2 - 4x + 12.

User Kris Adams
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Answer:

{-2/3, 2/3, 3}

Explanation:

The equation can be factored by grouping.

f(x) = (9x^3 -27x^2) +(-4x +12)

f(x) = 9x^2(x -3) -4(x -3)

f(x) = (9x^2 -4)(x -3)

We recognize the first factor as the difference of squares, so know it can be further factored to give ...

f(x) = (3x -2)(3x +2)(x -3)

The zeros are the values of x that make these factors be zero:

3x -2 = 0 ⇒ x = 2/3

3x +2 = 0 ⇒ x = -2/3

x -3 = 0 ⇒ x = 3

The zeros of the polynomial are x = -2/3, 2/3, 3.

Find the zeros of the polynomial function: f(x) = 9x^3 - 27x^2 - 4x + 12.-example-1
User Brooksbp
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