Sure, let's work through this polynomial expression step-by-step:
The given expression is:
[tex]\[ 10c^3 - 80c^5 - 5c^6 + 5c^7 \][/tex]
1. Identify the terms and their degrees:
- The term [tex]\(10c^3\)[/tex] has a degree of 3.
- The term [tex]\(-80c^5\)[/tex] has a degree of 5.
- The term [tex]\(-5c^6\)[/tex] has a degree of 6.
- The term [tex]\(5c^7\)[/tex] has a degree of 7.
2. Rewrite the expression in standard form:
- A polynomial is typically written in descending order of the degrees of its terms. Therefore, we arrange the terms from the highest degree to the lowest degree:
[tex]\[ 5c^7 - 5c^6 - 80c^5 + 10c^3 \][/tex]
Thus, the standardized form of the polynomial expression is:
[tex]\[ 5c^7 - 5c^6 - 80c^5 + 10c^3 \][/tex]
So, the simplified and ordered form of the polynomial is:
[tex]\[ 5c^7 - 5c^6 - 80c^5 + 10c^3 \][/tex]
This completes the solution! The polynomial expression is now neatly arranged in descending order of degrees.
