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.