To create a function or expression involving [tex]\(x\)[/tex], we start with the given expression:
[tex]\[ x^3 + x^5 - x^7 \][/tex]
Our goal is to rewrite this expression in a standard polynomial form. To do this, observe the individual terms and keep them as they are since they are already in their simplest form. Here, we have three monomials:
1. [tex]\( x^3 \)[/tex]
2. [tex]\( x^5 \)[/tex]
3. [tex]\( -x^7 \)[/tex]
Combining them together, we maintain the given expression as it is, but ordered typically from the highest degree term to the lowest degree term:
[tex]\[ -x^7 + x^5 + x^3 \][/tex]
So the expression [tex]\( x^3 + x^5 - x^7 \)[/tex] in a standard polynomial form is:
[tex]\[ -x^7 + x^5 + x^3 \][/tex]
This is the simplest form, and it is already written in terms of the variable [tex]\( x \)[/tex].
