Question

Solve by Factoring x^4-x^3+2x^2-4x-8=0

Answer 1

To solve the equation, we first group the terms and then factor out the common factors. After setting each factor equal to zero, we find the solutions to be x = ±√6, x = 0, and x = 1.

Step-by-step explanation:

We can solve the equation by factoring.

First, we group the terms:

x²(x² - x) + 2(x² - x) - 8 = 0

Now, we notice that each group of terms has a common factor of (x² - x), so we can factor it out:

(x² + 2 - 8)(x² - x) = 0

Simplifying further, we get:

(x² - 6)(x² - x) = 0

Now, we can set each factor equal to zero and solve for x:

x² - 6 = 0 or x² - x = 0

Solving the first equation, we get:

x = ±√6

For the second equation, we can factor out x:

x(x - 1) = 0

So, x = 0 or x = 1

Therefore, the solutions to the equation are:

x = ±√6, x = 0, x = 1