To find the degree of a polynomial, we need to identify the term with the highest exponent. The degree of the polynomial is the exponent in this term.
First, let's rewrite the polynomial by combining like terms:
[tex]\[ 5x^5 + 8x^2 + 2x - 3x^9 - 8x^4 - 4x^5 \][/tex]
We'll start by combining the terms with the same exponent:
1. Combine the [tex]\(x^5\)[/tex] terms:
[tex]\[ 5x^5 - 4x^5 = x^5 \][/tex]
So, the polynomial now includes [tex]\( x^5 \)[/tex].
2. There are no other like terms for [tex]\(8x^2\)[/tex], [tex]\(2x\)[/tex], [tex]\(-3x^9\)[/tex], and [tex]\(-8x^4\)[/tex], so these terms remain as they are.
Bringing everything together, the polynomial becomes:
[tex]\[ -3x^9 - 8x^4 + x^5 + 8x^2 + 2x \][/tex]
Now, let's identify the term with the highest exponent:
- The term [tex]\(-3x^9\)[/tex] has an exponent of 9.
- The term [tex]\(-8x^4\)[/tex] has an exponent of 4.
- The term [tex]\(x^5\)[/tex] has an exponent of 5.
- The term [tex]\(8x^2\)[/tex] has an exponent of 2.
- The term [tex]\(2x\)[/tex] has an exponent of 1.
Therefore, the highest exponent in the polynomial is 9.
Thus, the degree of the polynomial is:
[tex]\[ \boxed{9} \][/tex]
So, the correct answer is:
A. 9
