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].
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].
