Question

F(x) = (x – 1)3(x + 1)2

Answer 1

Ответ: x=6

Объяснение:

3х-3*2х+2=

6х-6=

6x=6

x=6

Answer 2

To understand the function F(x) = (x – 1)³(x + 1)², let's break it down step by step:

1. The function is composed of two terms, (x - 1)³ and (x + 1)², which are multiplied together.

2. (x - 1)³: This term represents a cubic polynomial. It means that (x - 1) is the base expression, and it's raised to the power of 3, resulting in a cube of (x - 1). When you expand this term, you get: (x - 1)³ = (x - 1)(x - 1)(x - 1) = (x² - 2x + 1)(x - 1) = x³ - 3x² + 3x - 1

3. (x + 1)²: This term represents a quadratic polynomial. It means that (x + 1) is the base expression, and it's raised to the power of 2, resulting in a square of (x + 1). When you expand this term, you get: (x + 1)² = (x + 1)(x + 1) = x² + 2x + 1

4. Now, to find the function F(x), we need to multiply the two terms together: F(x) = (x - 1)³(x + 1)² = (x³ - 3x² + 3x - 1)(x² + 2x + 1)

5. To get the final simplified form, we can use the distributive property of multiplication (FOIL method) or apply polynomial multiplication rules. After simplification, we get: F(x) = x⁵ - x⁴ - 5x³ + 5x² + 2x - 1

So, the function F(x) is a polynomial of degree 5 (quintic) and can be represented as F(x) = x⁵ - x⁴ - 5x³ + 5x² + 2x - 1.