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The given problem asks you to describe the end behavior of the polynomial \( p(x) = 3x^4 - 4x^3 - 10x \).

To analyze the end behavior, we need to focus on the highest degree term, which determines how the polynomial behaves as \( x \to \infty \) (positive infinity) or \( x \to -\infty \) (negative infinity).

### Step-by-step analysis:
1. **Degree of the polynomial**: The degree is 4 (from the term \( 3x^4 \)). This tells us the general shape of the graph will be similar to that of \( x^4 \), which is a symmetric U-shape.
   
2. **Leading coefficient**: The leading term is \( 3x^4 \), and the coefficient is positive (3). For even-degree polynomials with a positive leading coefficient, both ends of the graph will point upwards as \( x \to \infty \) and \( x \to -\infty \).

### End behavior:
- As \( x \to \infty \), \( p(x) \to \infty \).
- As \( x \to -\infty \), \( p(x) \to \infty \).

### Summary:
For the polynomial \( p(x) = 3x^4 - 4x^3 - 10x \), both ends of the graph will rise upwards, behaving similarly to the graph of \( x^4 \). This is because the leading term \( 3x^4 \) dominates the end behavior, and its positive coefficient means the graph opens upwards at both ends.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How does the degree of a polynomial affect its end behavior?
2. What happens to the end behavior if the leading coefficient is negative?
3. Can the lower degree terms (like \( -4x^3 \) or \( -10x \)) impact the end behavior?
4. How would the end behavior change if the degree of the polynomial was odd?
5. How can you determine the turning points of a polynomial like \( p(x) \)?

**Tip**: When analyzing polynomial end behavior, always focus on the highest degree term—it dominates the behavior as \( x \) becomes very large or very small.

Use your knowledge of the parent graphs to describe the end behavior of this polynomial: p(x) = 3x^4 - 4x^3 - 10x.

Understand how to describe the end behavior of the polynomial p(x) = 3x^4 - 4x^3 - 10x by analyzing the highest degree term. Learn the effects of the degree and leading coefficient on the graph's behavior as x approaches infinity.

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