The expression \( x^3 - 100 \) represents a cubic polynomial.

If you're looking to factor or simplify the expression:

1. **Factoring:**
   There isn't a simple factorization for this expression in terms of real numbers, but if you are working with complex numbers, it can be factored using the difference of cubes. However, since 100 isn't a perfect cube, no simple factorization using real numbers applies directly.

2. **Setting equal to zero (solving):**
   If you're trying to solve \( x^3 - 100 = 0 \), add 100 to both sides:

   \[
   x^3 = 100
   \]

   Now, take the cube root of both sides:

   \[
   x = \sqrt[3]{100}
   \]

   This simplifies to approximately \( x \approx 4.64 \).

3. **Graphical representation:**
   The graph of the function \( f(x) = x^3 - 100 \) would be a cubic curve with a vertical shift downwards by 100 units. The curve would cross the x-axis at \( x = \sqrt[3]{100} \).

Do you want more details or have any questions?

### Related Questions:
1. How do you factor a general cubic polynomial?
2. How can you approximate cube roots of numbers without a calculator?
3. How would the graph of \( x^3 - 100 \) compare to \( x^3 \)?
4. What are the properties of cubic functions?
5. Can you solve higher-degree polynomials like \( x^4 - 100 \) similarly?

### Tip:
Cube roots can be estimated using logarithms or more advanced numerical methods if precise results are needed!

Explore the cubic polynomial x^3 - 100, including how to solve the equation, factor using complex numbers, and analyze the graph. Suitable for students in Grades 10-12, this problem covers algebraic concepts like cubic polynomials and the cube root formula.

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