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**Find all the real solutions of**  
\[
x^3 - 16x^2 + 55x + 72 = 0.
\]

The real solutions provided are:
\[
x = 8, \quad x = -1, \quad \text{and} \quad x = 7.
\]

These are the three real roots of the cubic equation. To verify this, the equation can be factored or solved using methods such as synthetic division or the Rational Root Theorem. The given solutions satisfy the equation.

Would you like a detailed explanation of how these solutions were found?

Here are 5 related questions for deeper exploration:

1. How can you factor a cubic equation like this one?
2. What is synthetic division, and how can it be used to solve cubic equations?
3. What is the Rational Root Theorem, and how does it apply to this problem?
4. How can you verify that \(x = 8, x = -1, \text{ and } x = 7\) are the correct solutions?
5. What is the relationship between the factors of a polynomial and its roots?

**Tip**: When solving a cubic equation, always check for possible rational roots using factors of the constant term and leading coefficient!

Find all the real solutions of x^3 - 16x^2 + 55x + 72 = 0.

Explore the step-by-step process to solve the cubic equation x^3 - 16x^2 + 55x + 72 = 0. Learn how to find the real roots using the Rational Root Theorem and factorization methods. This problem is suitable for students in Grades 10-12.

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