What are the zeros of the polynomial function f(x) = x³ - 2x² - 24x?

Solution:

The given polynomial function is

f(x) = x³ - 2x² - 24x

Let us consider f(x) as 0

x³ - 2x² - 24x = 0

Taking out x as common

x(x² - 2x - 24) = 0

By splitting the middle term

x(x² - 6x + 4x - 24) = 0

Taking out the common terms

x [x(x - 6) + 4(x - 6)] = 0

x(x - 6)(x + 4) = 0

So we get

x = 0

x - 6 = 0 where x = 6

x + 4 = 0 where x = -4

So the zeros are x = 0, 6 and -4.

Therefore, the zeros of the polynomial function are x = 0, 6 and -4.

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What are the zeros of the polynomial function f(x) = x³ - 2x² - 24x?

Summary:

The zeros of the polynomial function f(x) = x³ - 2x² - 24x are x = 0, 6 and -4