Final answer:
The polynomial in standard form is option C: 8a³ + 10ab² - 12a²b³ because its terms are arranged in descending order of degree. Option C
Step-by-step explanation:
To determine which polynomial is in standard form, we look for the polynomial written with terms in descending order of degree (the highest power of the variable to the lowest), typically starting with the term that has the highest degree.
A: 4 + 3xy - 5xy³ + y⁴ is not in standard form because the terms aren't arranged by degree; the term with y⁴ should come first.
B: –x⁴ + x3y² + 7xy³ - 2y⁴x² is not in standard form because the terms are not solely arranged by degree; for multi-variable terms, the combined degree should be in descending order as well.
C: 8a³ + 10ab² - 12a²b³ is in standard form since the terms are arranged in descending order of degree based on the sum of the exponents of a and b in each term.
Therefore, the polynomial in standard form is option C: 8a³ + 10ab² - 12a²b³.