Final answer:
Upon reviewing each option and rearranging where necessary, option D, which is -6x⁴ + 3x³ + 4x² - 8, is the equation that is in standard form with a leading coefficient of -6.
Step-by-step explanation:
The student's question asks which of the given equations, when written in standard form, has a leading coefficient of -6. The standard form of a polynomial is when the terms are ordered by descending powers with the leading coefficient being the coefficient of the term with the highest power.
Let's examine each option:
- A. -6x + 2x² - 5 - This is not in standard form. When rearranged to 2x² - 6x - 5, the leading coefficient is 2, not -6.
- B. 6x² - 5x + 4 - This is in standard form, but the leading coefficient is 6, not -6.
- C. -8 + 4x² + 6x³ - Rearrange to 6x³ + 4x² - 8. The leading coefficient is 6, not -6.
- D. -6x⁴ + 3x³ + 4x² - 8 - This equation is already in standard form with the leading coefficient of -6.
Therefore, the correct option is D. -6x⁴ + 3x³ + 4x² - 8.