Answer :

We begin with the polynomial

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

Step 1. Combine Like Terms

Notice that there are two terms involving [tex]$x^5$[/tex]: [tex]$5x^5$[/tex] and [tex]$-4x^5$[/tex]. Combining them gives

[tex]$$
5x^5 - 4x^5 = x^5.
$$[/tex]

So, rewriting the polynomial with combined like terms, we have

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

Step 2. Identify the Degree

The degree of a polynomial is the highest exponent of [tex]$x$[/tex] that appears in the expression. In our simplified polynomial, the term with the highest power is

[tex]$$
-3x^9,
$$[/tex]

where the exponent is [tex]$9$[/tex].

Step 3. State the Final Answer

Thus, the degree of the given polynomial is

[tex]$$
9.
$$[/tex]

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Rewritten by : Barada