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Determine the degree of the polynomial.

[tex]x^4 - 8x + x^7 - 9x^5[/tex]

The degree of the polynomial is [tex]\square[/tex]

Answer :

To determine the degree of the polynomial [tex]\(x^4 - 8x + x^7 - 9x^5\)[/tex], we need to look at each term and find the highest power of [tex]\(x\)[/tex].

Here's a step-by-step solution:

1. Identify each term in the polynomial:
- The first term is [tex]\(x^4\)[/tex].
- The second term is [tex]\(-8x\)[/tex].
- The third term is [tex]\(x^7\)[/tex].
- The fourth term is [tex]\(-9x^5\)[/tex].

2. Determine the degree of each term:
- For [tex]\(x^4\)[/tex], the degree is 4.
- For [tex]\(-8x\)[/tex], the degree is 1.
- For [tex]\(x^7\)[/tex], the degree is 7.
- For [tex]\(-9x^5\)[/tex], the degree is 5.

3. Find the highest degree among all the terms:
- The degrees are 4, 1, 7, and 5.
- The highest degree is 7.

Therefore, the degree of the polynomial [tex]\(x^4 - 8x + x^7 - 9x^5\)[/tex] is [tex]\(\boxed{7}\)[/tex].

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