Use a graphing device to solve the inequality. Express your answer using interval notation, with the endpoints of the intervals rounded to two decimals.
x4 − 4x3 + 8x > 0

The function \( f(x) = x^4 - 4x^3 + 8x \) has the following x-intercepts (where \( f(x) = 0 \)):

\[
x = -1.24, \quad x = 0, \quad x = 2, \quad x = 3.24
\]

### 5. **Determine where the function is positive:**
Based on the graph and the intercepts, we can now analyze the intervals. The function is positive (i.e., \( f(x) > 0 \)) in the following intervals:

\[
(-\infty, -1.24) \cup (0, 2) \cup (3.24, \infty)
\]

Thus, the solution to the inequality \( x^4 - 4x^3 + 8x > 0 \) in interval notation is:

\[
(-\infty, -1.24) \cup (0, 2) \cup (3.24, \infty)
\]

Let me know if you need any further explanation or have any questions!

### Related Questions:
1. How do we handle inequalities with polynomials of degree higher than 2?
2. What are the benefits of graphing functions to solve inequalities?
3. Why are x-intercepts important when solving inequalities?
4. How does the behavior of the function change at critical points?
5. Can all polynomial inequalities be solved using graphing devices?

### Tip:
When solving inequalities, always check the behavior of the function at and between critical points to determine where the inequality holds true.

Use a graphing device to solve the inequality. Express your answer using interval notation, with the endpoints of the intervals rounded to two decimals.
x^4 − 4x^3 + 8x > 0

Learn how to solve the polynomial inequality x^4 - 4x^3 + 8x > 0 using graphing. This solution covers key algebra concepts like polynomial roots, sign chart analysis, and interpreting positive and negative intervals. Ideal for students in Grades 10-12.

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