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Polynomial A has degree​ 2; Polynomial B has degree 4. What can you determine about the name and degree of the sum of the polynomials and the difference of the polynomials if Polynomial A is a binomial and Polynomial B is a​ monomial?

1. What can you determine about the name of the sum and difference of the polynomials if Polynomial A is a binomial and Polynomial B is a​ monomial? Choose the correct answer below.
A.
The data is insufficient as the Polynomial B has a higher degree and might not have a term of degree 2.
B.
The sum of the polynomials gives a​ trinomial, and the difference gives a binomial.
C.
The sum of the polynomials gives a​ binomial, and the difference gives a monomial.
D.
Both the sum and difference of the polynomials are trinomials.

2 Answers

6 votes
If Polynomial A is a binomial of degree 2 and Polynomial B is a monomial of degree 4, we can determine the name and degree of the sum and difference of these polynomials.
1. Name and degree of the sum:
When we add the two polynomials together, the resulting polynomial will have the same name as the original polynomials. Since Polynomial A is a binomial, the sum of the polynomials will also be a binomial. The degree of the sum will be the same as the degree of the polynomial with the higher degree, which in this case is Polynomial B with a degree of 4.
Therefore, the sum of the polynomials will also have a degree of 4.
2. Name and degree of the difference:
When we subtract Polynomial A from
Polynomial B, the resulting polynomial will have the same name as the original polynomials. Since Polynomial A is a binomial, the difference of the polynomials will also be a binomial. The degree of the difference will be the same as the degree of the polynomial with the higher degree, which again is Polynomial B with a degree of 4.
Therefore, the difference of the polynomials will also have a degree of 4.
Based on this information, the correct answer is:
B. The sum of the polynomials gives a trinomial, and the difference gives a binomial.
User Ken Joyner
by
7.9k points
2 votes

Answer: i think its c because i jst guessed

Explanation:

User TLJ
by
8.3k points

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