The standard form of a polynomial function is one where the terms are ordered by degree, from the highest to the lowest power of the variable. For example, $ax^n + bx^{n-1} + \dots + k$ where the terms are written in descending order of the powers of the variable.

Let’s put each polynomial in standard form:

1. $-10n - 6 - 8n^3 + 2n^2$

   Standard Form: $-8n^3 + 2n^2 - 10n - 6$

2. $1 - 2r^4 + 5r^2 + 5r^3$

   Standard Form: $-2r^4 + 5r^3 + 5r^2 + 1$

3. $-3b^3 - 7b^6 - 6b$

   Standard Form: $-7b^6 - 3b^3 - 6b$

4. $-8x^2 + 5x - 4x^4$

   Standard Form: $-4x^4 - 8x^2 + 5x$

5. $5x^2 + 4x^6 - 3x^4$

   Standard Form: $4x^6 - 3x^4 + 5x^2$

6. $-4v^6 - 5v^3 + 6v^4$

   Standard Form: $-4v^6 + 6v^4 - 5v^3$

7. $-1 + 8n^2 + 5n$

   Standard Form: $8n^2 + 5n - 1$

8. $4r^3 - 2r^2 + 4 - 5r$

   Standard Form: $4r^3 - 2r^2 - 5r + 4$

9. $4v^2 - 7 + 6v^3$

   Standard Form: $6v^3 + 4v^2 - 7$

10. $7x^6 - x^2 - 7$

    Standard Form: $7x^6 - x^2 - 7$

Would you like any detailed explanation on these steps?

Here are some additional questions for practice:

1. How would you convert $7y^5 + 3y - y^4 + 2$ to standard form?
2. What is the standard form of $-6x + x^3 - 9 + 4x^2$?
3. How do you arrange the polynomial $8a - 5a^2 + 7a^4$ into standard form?
4. If you had a polynomial $12t + 9t^5 - 2t^3 + t^2$, what would be the standard form?
5. How can you write $2n - 9n^4 + 4n^2 + 1$ in standard form?

Tip: To quickly determine the standard form of any polynomial, first identify the highest power of the variable, then arrange all terms in descending order by the exponent.