I see you've uploaded an image containing a table to be completed with information about polynomials. I'll extract the content and help complete the table.

Here is the given information and the missing parts of the table:

Table Fields

1. Polynomial: The given expression.
2. Standard Form: The polynomial written in descending order of powers.
3. Degree: The highest power of $x$ in the polynomial.
4. Number of Terms: The number of separate terms in the polynomial.
5. Name: Classification based on degree and number of terms.

Completed Table:

I'll process and fill out the rest of the table for you.

1. $3 - 7x - 9x^2$

• Standard Form: $-9x^2 - 7x + 3$
• Degree: 2nd (Quadratic)
• Number of Terms: 3
• Name: Quadratic Trinomial (already filled).

2. $5 - 6x^3$

• Standard Form: $-6x^3 + 5$
• Degree: 3rd (Cubic)
• Number of Terms: 2
• Name: Cubic Binomial.

3. $-4$

• Standard Form: $-4$
• Degree: 0 (Constant)
• Number of Terms: 1
• Name: Constant Monomial.

4. $-10 + 5x$

• Standard Form: $5x - 10$
• Degree: 1st (Linear)
• Number of Terms: 2
• Name: Linear Binomial.

5. $8x - 2 - 6x^3$

• Standard Form: $-6x^3 + 8x - 2$
• Degree: 3rd (Cubic)
• Number of Terms: 3
• Name: Cubic Trinomial.

Let me know if you’d like a more detailed explanation for any of the fields!

Related Questions:

1. How can you determine the degree of a polynomial quickly?
2. What are the naming conventions for polynomials based on terms and degree?
3. How do you standardize polynomials effectively?
4. What is the significance of the highest degree in a polynomial equation?
5. How would this table change if additional variables were introduced (e.g., $y$)?

Tip: Always arrange polynomials in descending order of the exponents to standardize them.