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The given polynomial equation is:

\[
P(x) = (x - 2)(x + 1)(x - 3)(x + 4) = 0
\]

To find the solutions (or roots) of the equation \(P(x) = 0\), we need to set each factor equal to zero and solve for \(x\):

1. \(x - 2 = 0 \quad \Rightarrow \quad x = 2\)
2. \(x + 1 = 0 \quad \Rightarrow \quad x = -1\)
3. \(x - 3 = 0 \quad \Rightarrow \quad x = 3\)
4. \(x + 4 = 0 \quad \Rightarrow \quad x = -4\)

Thus, the solutions to the equation are:

\[
x = 2, \quad x = -1, \quad x = 3, \quad x = -4
\]

The correct answer is the second option:

\[
x = 2, \, x = -1, \, x = -3, \, x = -4
\]

Do you want more details or have any questions? Here are five related questions for further practice:

1. How would you factor a cubic polynomial to find its roots?
2. What are the possible types of roots (real, complex) for a polynomial of degree 4?
3. How do you determine the multiplicity of a root in a polynomial?
4. If one root of a polynomial is complex, what can you say about the other roots?
5. How can you use the Rational Root Theorem to help solve polynomial equations?

**Tip:** Always check the sign of each term when setting factors equal to zero; it's easy to overlook a negative sign.

Si tienes un polinomio P(x) de grado 4 y su forma factorizada es (x - 2)(x + 1)(x - 3)(x + 4) = 0, ¿Cuáles son las soluciones (raíces) de la ecuación P(x) = 0?

Learn how to solve the degree 4 polynomial equation (x - 2)(x + 1)(x - 3)(x + 4) = 0 by factoring. This problem demonstrates key concepts in solving polynomial equations, including the Zero Product Property and finding the roots of polynomials. Suitable for students in Grades 10-12.

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