Question

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

Answer 1

- 6 x - 182

Explanation:

Answer 2

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.