To determine which polynomial is in standard form, we need to identify the one that fulfills the criteria of a standard polynomial form, which typically means the terms are ordered from highest to lowest degree. Let’s examine each option:
1. [tex]\(4xy + 3x^3y^5 - 2x^5y^7 + 4x^7y^9\)[/tex]
- This polynomial is not in standard form because the terms are not ordered by their degree from highest to lowest.
2. [tex]\(2x^5y^7 + 7y - 8x^2y^5 - 12xy^2\)[/tex]
- This polynomial is also not in standard form due to the incorrect ordering of terms by degree.
3. [tex]\(5x^5 - 9x^2y^2 - 3xy^3 + 6y^5\)[/tex]
- This polynomial is in standard form. The terms are ordered by decreasing degree:
- [tex]\(5x^5\)[/tex] (degree 5)
- [tex]\(-9x^2y^2\)[/tex] (degree 4)
- [tex]\(-3xy^3\)[/tex] (degree 4)
- [tex]\(6y^5\)[/tex] (degree 5)
4. [tex]\(7x^7y^2 + 5x^{11}y^5 - 3xy^2 + 2\)[/tex]
- This polynomial is not in standard form due to the incorrect ordering of terms by degree.
Hence, the polynomial in standard form is:
[tex]\[ 5x^5 - 9x^2y^2 - 3xy^3 + 6y^5 \][/tex]
