Which description best defines the standard form of a polynomial?

• A. Write the polynomial with terms arranged in ascending order of exponents (lowest degree to highest), without combining like terms.
• B. Write the polynomial with all terms ordered alphabetically by variable name, regardless of exponent.
• C. Write the polynomial as a product of its factors only (factored form).
• D. Write the polynomial with terms arranged in descending order of exponents (highest degree to lowest), combining like terms.

Answer: (D)

Verified step by step guidance

1. Understand that the standard form of a polynomial means arranging the terms in a specific order based on the degree (exponent) of each term.
2. Recall that the degree of a term is the exponent of the variable in that term, and the degree of the polynomial is the highest exponent present.
3. Recognize that in standard form, terms are written in descending order of exponents, starting with the term having the highest degree and ending with the constant term (degree zero).
4. Combine like terms, which means adding or subtracting coefficients of terms that have the same variable raised to the same power, to simplify the polynomial.
5. Therefore, the standard form of a polynomial is the expression written with terms ordered from highest to lowest degree, with all like terms combined.