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The integer solutions to the equation \( x^4 - x^3 = 4x^2 - 4x \) are:

\[
x = -2, 0, 1, 2
\]

In increasing numerical order, the solutions are: \(-2, 0, 1, 2\).

Would you like more details on the factoring process or any other explanations?

Here are 5 related questions:
1. How do you factor a polynomial with higher powers of \( x \)?
2. What happens if an equation has non-integer solutions?
3. How do you solve equations with complex solutions?
4. Can this method be used for cubic or quintic polynomials?
5. What are other techniques besides factoring for solving polynomial equations?

**Tip:** Always check if you can factor out common terms before trying other methods of solving equations.

Find the integer solutions to this equation by factoring in standard form: x^4 - x^3 = 4x^2 - 4x

Learn how to solve the polynomial equation x^4 - x^3 = 4x^2 - 4x by factoring. This problem covers key algebraic concepts such as factoring and the Zero Product Property. Suitable for high school students in Grades 10-12.

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