Respuesta :
Degree of a polynomial gives the highest power of its terms. Yes there is a difference between the degrees of sum and difference of the polynomials.
What is degree of a polynomial?
Degree of a polynomial is the highest power that its terms pertain(for multi-variables, the power of term is addition of power of variables in that term).
Thus, in [tex]x^3 + 3x^2 + 5[/tex], the degree of the polynomial is 3 as the highest power in its terms is 3.
(power and exponent are same thing)
What are like terms?
Those terms which have same variables raised with same powers.
For example, [tex]x^3[/tex] and [tex]3x^3[/tex] are like terms since variable is same, and it is raised to same power 3.
For example [tex]4x^2[/tex] and [tex]x^3[/tex] are not like terms as the variables are same but powers aren't same.
The given polynomials are:
[tex]c(x) = x^7 + 3x^5 + 3x + 1\\\\p(x) = x^7 + 5x + 10[/tex]
Their sum is
[tex]c(x) + p(x) = x^7 + 3x^5 + 3x + 1 + x^7 + 5x + 10 = (1+1)x^7 + 3x^5 + (3+5)x + 11\\\\c(x) + p(x) = 2x^7 + 3x^5 + 8x + 11[/tex]
(only like terms' coefficients can be added (or subtracted) for addition or subtraction of them )
The sum's degree is 7
Their difference is:
[tex]c(x) - p(x) = x^7 + 3x^5 + 3x + 1 - x^7 -5x - 10 = (1-1)x^7 + 3x^5 +(3-5)x -9\\\\c(x) - p(x) = 3x^5 - 2x - 9[/tex]
Difference's degree is 5
Thus, both's degrees are not same.
Thus, Yes there is a difference between the degrees of sum and difference of the polynomials.
Learn more about subtraction of polynomials here:
https://brainly.com/question/9351663
