Final answer:
The terms that could be added to '+875 - 3r^3' to be in standard form are Options C) 0 and E) -r, because they have equal or higher degree terms. B) 6 and D) -875 can technically be added, but they would not keep '-3r^3' as the leading term.
Step-by-step explanation:
The student is seeking an answer to which terms could be used as the first term of an expression to create a polynomial written in standard form. The expression provided is '+875 - 3r^3'. The following options are listed as potential first terms: A) 55, B) 6, C) 0, D) -875, E) -r, F) 41.
To be in standard form, a polynomial must have its terms written in order of decreasing degree. Since the given term is '-3r^3', we need a term with a degree higher than 3 or equal to 3 to ensure it remains in standard form. Here are the suitable options:
- Option A) 55 is not appropriate as it is a constant term with a degree of 0.
- Option B) 6 is also a constant with a degree of 0 and is not suitable.
- Option C) 0 can be used because it will not affect the leading term (which is '-3r^3').
- Option D) -875 is not suitable as it's a constant term with a degree of 0.
- Option E) -r is suitable as it has a degree of 1.
- Option F) 41 is also a constant and not suitable.
Therefore, the terms that can be used are: C) 0 and E) -r. It should be noted that B) 6 and D) -875 are technically correct too, but these options are not the best choices as they would make '-3r^3' not be the leading term.