Questions: f x=x^3-4 x^2-25 x+100

Transcript text: $f x=x^{3}-4 x^{2}-25 x+100$

Solution

Step 1: Define the Polynomial

We start with the polynomial function given by

\[ f(x) = x^{3} - 4x^{2} - 25x + 100. \]

Step 2: Factor the Polynomial

Next, we factor the polynomial into its linear components. The factorization of $ f(x) $ is

\[ f(x) = (x - 5)(x - 4)(x + 5). \]

Step 3: Verify the Factorization

To ensure the factorization is correct, we can expand the factors:

\[ (x - 5)(x - 4)(x + 5). \]

First, we can multiply $ (x - 5)(x + 5) $:

\[ (x - 5)(x + 5) = x^{2} - 25. \]

Now, we multiply this result by $ (x - 4) $:

\[ (x^{2} - 25)(x - 4) = x^{3} - 4x^{2} - 25x + 100. \]

This confirms that the factorization is correct.

$\boxed{(x - 5)(x - 4)(x + 5)}$

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