To determine which polynomial is written in standard form, we must ensure that the terms are ordered in descending powers of [tex]\(x\)[/tex]. Let's examine and order each given polynomial:
1. [tex]\(2 x^2 + 3 x^4 + 10 x^6\)[/tex]:
- Terms: [tex]\(2 x^2\)[/tex], [tex]\(3 x^4\)[/tex], [tex]\(10 x^6\)[/tex]
- Standard form: [tex]\(10 x^6 + 3 x^4 + 2 x^2\)[/tex]
2. [tex]\(4 x^4 + 6 x^3 + 10 x^4\)[/tex]:
- Terms: [tex]\(4 x^4\)[/tex], [tex]\(6 x^3\)[/tex], [tex]\(10 x^4\)[/tex]
- Combine like terms: [tex]\(4 x^4 + 10 x^4 = 14 x^4\)[/tex]
- Standard form: [tex]\(14 x^4 + 6 x^3\)[/tex]
3. [tex]\(-3 x^8 + 9 x^2 + 10 x\)[/tex]:
- Terms: [tex]\(-3 x^8\)[/tex], [tex]\(9 x^2\)[/tex], [tex]\(10 x\)[/tex]
- Standard form: [tex]\(-3 x^8 + 9 x^2 + 10 x\)[/tex] (already in descending order)
4. [tex]\(-7 x^6 + x^3 + 10 x^8\)[/tex]:
- Terms: [tex]\(-7 x^6\)[/tex], [tex]\(x^3\)[/tex], [tex]\(10 x^8\)[/tex]
- Standard form: [tex]\(10 x^8 - 7 x^6 + x^3\)[/tex]
After examining each polynomial, we see that the third polynomial [tex]\( -3 x^8 + 9 x^2 + 10 x \)[/tex] is already written in descending order of powers of [tex]\( x \)[/tex].
Therefore, the polynomial that is written in standard form is:
[tex]\[
\boxed{-3 x^8 + 9 x^2 + 10 x}
\][/tex]
