Final answer:
The correct term to complete the polynomial in standard form is A) x²y², as it fills the gap in the sequence of degrees between the other terms, resulting in a standard form polynomial 8x³y² - x²y² + 3xy² - 4y³.
Step-by-step explanation:
The student is asking for the appropriate term to complete a polynomial in standard form. The given expression is 8x³y²-____+3xy²-4y³. To create a fully simplified polynomial in standard form, we should look for a term that, when combined with the other terms, results in a polynomial with positive degrees in descending order without any gaps in the degree sequence. Since we already have the terms with x³, xy², and y³, we need a term that would represent the x²y² component. Therefore, the correct answer is A) x²y².
To reach the answer, I considered the rule that polynomials in standard form must have terms ordered by decreasing degrees of the variable. The gaps between the degrees of the terms must also be filled. Given the highest degree term is x³y², the term x²y² correctly completes the sequence, resulting in a standard form polynomial: 8x³y² - x²y² + 3xy² - 4y³.