Answer :

To determine the degree of the polynomial, we first need to simplify it by combining like terms. Let's look at the polynomial:

[tex]\[ 5x^5 + 8x^2 + 2x - 3x^9 - 8x^4 - 4x^5 \][/tex]

1. Identify and combine like terms:
- Consider the [tex]\(x^5\)[/tex] terms: [tex]\(5x^5\)[/tex] and [tex]\(-4x^5\)[/tex]. Combine them:
[tex]\[ 5x^5 - 4x^5 = 1x^5 \][/tex]

Now, rewrite the polynomial with the simplified terms:

[tex]\[ -3x^9 + 1x^5 - 8x^4 + 8x^2 + 2x \][/tex]

2. Determine the highest power of x:
- The degree of a polynomial is the highest exponent of [tex]\(x\)[/tex] present in the polynomial.
- In the simplified polynomial, the terms and their degrees are:
- [tex]\(-3x^9\)[/tex] with a degree of 9
- [tex]\(1x^5\)[/tex] with a degree of 5
- [tex]\(-8x^4\)[/tex] with a degree of 4
- [tex]\(8x^2\)[/tex] with a degree of 2
- [tex]\(2x\)[/tex] with a degree of 1

The highest degree among these terms is [tex]\(9\)[/tex], which comes from the term [tex]\(-3x^9\)[/tex].

Therefore, the degree of the polynomial is [tex]\(9\)[/tex].

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Rewritten by : Barada