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]
[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]
