Answer :

To find the degree of the polynomial [tex]\( y = 4x^9 + 1 - 5x^6 - 4x^8 \)[/tex]:

1. Identify the terms of the polynomial and their respective degrees:
- The term [tex]\( 4x^9 \)[/tex] has a degree of 9.
- The term [tex]\( 1 \)[/tex] has a degree of 0 (since it is a constant).
- The term [tex]\( -5x^6 \)[/tex] has a degree of 6.
- The term [tex]\( -4x^8 \)[/tex] has a degree of 8.

2. Determine the highest degree among all the terms:
- The degrees of the terms are: 9, 0, 6, and 8.

3. The highest degree among these is 9.

Thus, the degree of the polynomial [tex]\( y = 4x^9 + 1 - 5x^6 - 4x^8 \)[/tex] is [tex]\( 9 \)[/tex].

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