determining the degree and maximum number of terms of a sum or difference\ncory writes the polynomial (…

determining the degree and maximum number of terms of a sum or difference\ncory writes the polynomial ( x^{7}+3 x^{5}+3 x + 1 ). melissa writes the polynomial ( x^{7}+5 x + 10 ). is there a difference between the degree of the sum and the degree of the difference of the polynomials?\nadding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 7.\nadding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 5.\nadding their polynomials together results in a polynomial with degree 14, but subtracting one polynomial from the other results in a polynomial with degree 5.\nadding their polynomials together results in a polynomial with degree 7, but subtracting one polynomial from the other results in a polynomial with degree 5.

determining the degree and maximum number of terms of a sum or difference\ncory writes the polynomial ( x^{7}+3 x^{5}+3 x + 1 ). melissa writes the polynomial ( x^{7}+5 x + 10 ). is there a difference between the degree of the sum and the degree of the difference of the polynomials?\nadding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 7.\nadding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 5.\nadding their polynomials together results in a polynomial with degree 14, but subtracting one polynomial from the other results in a polynomial with degree 5.\nadding their polynomials together results in a polynomial with degree 7, but subtracting one polynomial from the other results in a polynomial with degree 5.

Answer

Explanation:

Step1: Find the sum of the polynomials

Let (P(x)=x^{7}+3x^{5}+3x + 1) and (Q(x)=x^{7}+5x + 10). The sum (S(x)=P(x)+Q(x)=(x^{7}+3x^{5}+3x + 1)+(x^{7}+5x + 10)) (=x^{7}+x^{7}+3x^{5}+(3x + 5x)+(1 + 10)) (=2x^{7}+3x^{5}+8x+11). The degree of a polynomial is the highest power of the variable. Here, the degree of (S(x)) is (7) (since the highest - power term is (2x^{7})).

Step2: Find the difference of the polynomials

The difference (D(x)=P(x)-Q(x)=(x^{7}+3x^{5}+3x + 1)-(x^{7}+5x + 10)) (=x^{7}-x^{7}+3x^{5}+(3x-5x)+(1 - 10)) (=3x^{5}-2x - 9). The degree of (D(x)) is (5) (since the highest - power term is (3x^{5})).

Answer:

Adding their polynomials together results in a polynomial with degree 7, but subtracting one polynomial from the other results in a polynomial with degree 5.