Certainly! Let's reorganize the given polynomial \( 7c^2 - 5c^4 + c^6 \) in descending powers of the variable \( c \).
1. Identify the degrees of each term:
- \( 7c^2 \) has a degree of 2.
- \( -5c^4 \) has a degree of 4.
- \( +c^6 \) has a degree of 6.
2. Arrange the terms in descending order based on their degrees:
- The highest degree is 6, so \( c^6 \) comes first.
- The next highest degree is 4, so \( -5c^4 \) comes next.
- The lowest degree of the given terms is 2, so \( 7c^2 \) comes last.
Putting it all together, the polynomial written in descending powers of the variable \( c \) is:
[tex]\[ c^6 - 5c^4 + 7c^2 \][/tex]
Thus, the rearranged polynomial is:
[tex]\[ c^6 - 5c^4 + 7c^2 \][/tex]
