Questions: Find the real zeros of f. Use the real zeros to factor f. f(x) = x^3 - 5x^2 - 61x - 55 The real zero(s) of f is/are -5, -1, 11

Find the real zeros of f. Use the real zeros to factor f. f(x) = x^3 - 5x^2 - 61x - 55 The real zero(s) of f is/are -5, -1, 11
Transcript text: Find the real zeros of f . Use the real zeros to factor f . \[ f(x)=x^{3}-5 x^{2}-61 x-55 \] The real zero(s) of f is/are $-5,-1,11$
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Solution

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Solution Steps

Step 1: Find the real zeros of f(x)

Given the function f(x) = x³ - 5x² - 61x - 55, we find the real zeros by setting f(x) = 0 and solving for x. The given zeros are -5, -1, and 11.

Step 2: Use the real zeros to factor f(x)

Since the real zeros are -5, -1, and 11, the factors of f(x) are (x - (-5)), (x - (-1)), and (x - 11). Simplifying these factors, we get (x + 5), (x + 1), and (x - 11).

Final Answer

The factored form of f(x) is f(x) = (x + 5)(x + 1)(x - 11).

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