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F(x) = (x + 2)(x - 1)[x - (4 + 3)][x - (4 - 31)]

F(x) = (x + 2)(x - 1)[x - (4 + 3)][x - (4 - 31)]-example-1

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3 votes

Answer:

- 6 x - 182

Explanation:

User Neomega
by
7.6k points
4 votes

The expanded form of the function f(x) is:


\[ f(x) = x^4 - 7x^3 + 15x^2 + 41x - 50 \]

This is the simplified polynomial form of the given function.

The function f(x) provided in the image is a product of four factors:
\( (x + 2) \), \( (x - 1) \), \( (x - (4 + 3i)) \), and \( (x - (4 - 3i)) \). To simplify this function, we need to expand the product of these factors. Here are the steps involved:

1. Recognize the Complex Conjugate Pair: The factors
\( (x - (4 + 3i)) \) and \( (x - (4 - 3i)) \) are a pair of complex conjugates. When multiplied together, they will result in a quadratic expression with real coefficients.

2. Multiply the Complex Conjugate Pair: We can multiply
\( (x - (4 + 3i)) \)and
\( (x - (4 - 3i)) \) to obtain a quadratic polynomial.

3. Multiply the Remaining Real Factors: After obtaining the quadratic polynomial from the complex conjugate pair, we can then multiply it by the remaining factors (x + 2) and (x - 1) to get the expanded form of the function.

4. Expand the Entire Expression: The final step is to expand the entire expression to get f(x) in standard polynomial form.

User Kylekeesling
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8.0k points

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