Question

Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Select five options.

+8r^2s^4 - 3r^3s^3

A) 8r^2s^4
B) -3r^3s^3
C) 355
D) -s^6
E) 0-r^5s

Answer 1

The terms that could serve as the first term of the polynomial in standard form are those with the highest degree or those that maintain descending order: -3r^3s^3, 0-r^5s, -s^6, 8r^2s^4, and 355.

Step-by-step explanation:

To write the expression in standard form, we need to order the terms so that the powers of the variables decrease from left to right. Therefore, the first term should have the highest degree (the sum of the exponents for r and s in each term), and we should select terms that maintain this order when combined with the existing terms +8r^2s^4 - 3r^3s^3. Here are the appropriate choices:

• -3r^3s^3 has the highest degree of 6 (3 for r and 3 for s), matching one of the given terms.
• 0-r^5s has the degree of 6 (5 for r and 1 for s), which fits the standard form criteria.
• -s^6 has the degree of 6, which fits the standard form criteria.
• 8r^2s^4 has the degree of 6 (2 for r and 4 for s), which fits the standard form criteria.
• 355 is a constant term and can serve as the last term in standard form, as it does not affect the ordering of the higher degree terms.

The remaining terms in the expression should follow in decreasing order of degree to comply with the definiton of a polynomial in standard form.