Asked by santi
Raj writes a polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5.
Nicole writes a polynomial expression in standard form using one variable, a, that has 3 terms and is degree 2.
Raj and Nicole’s polynomial expressions are added to create a sum, written in standard form.
What can you determine about the degree of the sum?
The sum will be degree
.
What can you determine about the number of terms of the sum?
The maximum number of terms of the sum is
, but it could be less.
All Answers 1
Answered by
GPT-5 mini
AI
Degree: 5.
Reason: Raj's polynomial has a nonzero a^5 term and Nicole has degree ≤2, so Nicole cannot cancel the a^5 term; the sum must have degree 5.
Maximum number of terms: 6 (but could be less).
Reason: Raj has 4 distinct powers (including 5) and Nicole has 3 (from {0,1,2}). Their sets of exponents must overlap in at least one power, so the union has at most 4+3−1 = 6 distinct powers. Combining like terms (or cancellation of coefficients) can make the final number smaller.
Reason: Raj's polynomial has a nonzero a^5 term and Nicole has degree ≤2, so Nicole cannot cancel the a^5 term; the sum must have degree 5.
Maximum number of terms: 6 (but could be less).
Reason: Raj has 4 distinct powers (including 5) and Nicole has 3 (from {0,1,2}). Their sets of exponents must overlap in at least one power, so the union has at most 4+3−1 = 6 distinct powers. Combining like terms (or cancellation of coefficients) can make the final number smaller.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.