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------------------------------------------------ The degree of the term [tex]$4x^6$[/tex] is: [tex]\square[/tex]
The degree of the term [tex]$-2x^9$[/tex] is: [tex]\square[/tex]
The degree of the term [tex]$1$[/tex] is: [tex]\square[/tex]
The degree of the term [tex]$2x^8$[/tex] is: [tex]\square[/tex]
The degree of the polynomial [tex]$4x^6 - 2x^9 + 1 + 2x^8$[/tex] is: [tex]\square[/tex]

Sure! Let's break it down step-by-step to find the degree of each term and the entire polynomial.

1. Degree of a Term:
- The degree of a term is the highest power of the variable in that term.

2. Analyzing Each Term:

- Term [tex]$4x^6$[/tex]:
The variable [tex]$ x $[/tex] is raised to the power of 6, so the degree of the term is 6.

- Term [tex]$-2x^9$[/tex]:
The variable [tex]$ x $[/tex] is raised to the power of 9, so the degree of the term is 9.

- Term 1:
This is a constant term, which can be thought of as [tex]$ 1 \times x^0 $[/tex]. The power of the variable here is 0, so the degree of the term is 0.

- Term [tex]$2x^8$[/tex]:
The variable [tex]$ x $[/tex] is raised to the power of 8, so the degree of the term is 8.

3. Degree of the Polynomial:
- The degree of a polynomial is the highest degree of any term in the polynomial.
- We have the degrees: 6, 9, 0, and 8 for the terms respectively.
- The highest degree among these is 9.

Therefore, the solution is:
- The degree of the term [tex]$ 4x^6 $[/tex] is: 6
- The degree of the term [tex]$ -2x^9 $[/tex] is: 9
- The degree of the term 1 is: 0
- The degree of the term [tex]$ 2x^8 $[/tex] is: 8
- The degree of the polynomial [tex]$ 4x^6 - 2x^9 + 1 + 2x^8 $[/tex] is: 9