Question

Find the factorization of f(x)
f(x) =-2x⁴ + 12x³+ 16x²- 12x– 14

Answer 1

The factorization of the given expression f(x)f(x) = -2x⁴ + 12x³ + 16x² - 12x - 14 is -1(x - 2)(x + 1)(x - 7)(x + 1).

Step-by-step explanation:

The factorization of the given expression f(x)f(x) = -2x⁴ + 12x³ + 16x² - 12x - 14 can be found by factoring out common factors and then using the quadratic formula for the remaining quadratic expression. Let's break it down step by step:

1. First, factor out -1 from the expression: f(x)f(x) = (-1)(2x⁴ - 12x³ - 16x² + 12x + 14)
2. Now, let's factor the quadratic expression inside the parentheses using the quadratic formula or any other method. The factors are: (x - 2)(x + 1)(x - 7)(x + 1)
3. Combining the factors, we get: f(x)f(x) = -1(x - 2)(x + 1)(x - 7)(x + 1)

So, the factorization of f(x)f(x) = -2x⁴ + 12x³ + 16x² - 12x - 14 is f(x)f(x) = -1(x - 2)(x + 1)(x - 7)(x + 1).