https://file.aiquickdraw.com/mathbot/file/1726259648105vjgavb0g.jpg

The image contains the following mathematical expression and problem:

Given:
\[
q(x) = x^4 - 5x^3 - 3x
\]
You are tasked with finding \(q(1)\) and \(q(-3)\), with the answers provided as:
\[
q(1) = 1
\quad \text{and} \quad
q(-3) = -219
\]

### Let's verify the solutions:

1. **For \( q(1) \):**
   \[
   q(1) = 1^4 - 5(1^3) - 3(1)
   \]
   Simplifying:
   \[
   q(1) = 1 - 5 - 3 = 1
   \]
   This is correct.

2. **For \( q(-3) \):**
   \[
   q(-3) = (-3)^4 - 5(-3)^3 - 3(-3)
   \]
   Simplifying:
   \[
   q(-3) = 81 - 5(-27) - 3(-3) = 81 + 135 + 9 = 225
   \]
   However, there seems to be an issue here, as the given solution is \( q(-3) = -219 \), but the calculated result is \( 225 \).

It appears there might be an error in the provided solution for \( q(-3) \). If you'd like to further clarify or explore where this discrepancy might have arisen, let me know!

---

Would you like any additional details or clarifications? Here are five related questions for further practice:

1. What is \( q(2) \) for the given polynomial \( q(x) = x^4 - 5x^3 - 3x \)?
2. How does the degree of a polynomial affect the behavior of its graph?
3. Can you factor the polynomial \( x^4 - 5x^3 - 3x \)?
4. What are the critical points of \( q(x) \), where \( q'(x) = 0 \)?
5. How does the end behavior of \( q(x) \) behave as \( x \to \infty \) or \( x \to -\infty \)?

### Tip:
When evaluating polynomials, it's often helpful to group terms and simplify systematically, especially when substituting negative values for \(x\).

If q(x) = x^4 - 5x^3 - 3x, find q(1) and q(-3).

Learn how to evaluate the polynomial function q(x) = x^4 - 5x^3 - 3x at specific values of x. In this example, we compute q(1) and q(-3) step-by-step, demonstrating substitution and simplification techniques.

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