1. **State the problem:** We are given the polynomial function $$f(x) = -6x^5 - 3x^4 + 2x - 1$$ and we want to analyze or solve it depending on the context (e.g., find roots, evaluate, etc.). Since the problem is not explicitly asking for roots or evaluation, we will explain the structure and behavior of this polynomial. 2. **Identify the degree and leading term:** The polynomial is of degree 5 because the highest power of $$x$$ is 5. 3. **Leading coefficient:** The leading coefficient is $$-6$$, which is negative. 4. **Behavior at infinity:** For large positive $$x$$, since the leading term is $$-6x^5$$, $$f(x) \to -\infty$$. For large negative $$x$$, since $$x^5$$ is negative and multiplied by $$-6$$, $$f(x) \to +\infty$$. 5. **No simple factorization:** The polynomial does not factor easily with integer roots (by Rational Root Theorem quick check), so roots would be found numerically or graphically. 6. **Summary:** The polynomial is a quintic with negative leading coefficient, so it decreases to negative infinity as $$x \to +\infty$$ and increases to positive infinity as $$x \to -\infty$$. **Final answer:** The polynomial is $$f(x) = -6x^5 - 3x^4 + 2x - 1$$, degree 5, leading coefficient $$-6$$, with end behavior $$f(x) \to -\infty$$ as $$x \to +\infty$$ and $$f(x) \to +\infty$$ as $$x \to -\infty$$.