Answer:
The difference of the degrees of the polynomials p (x) and q (x) is 1.
Step-by-step explanation:
A polynomial function is made up of two or more algebraic terms, such as p (x), p (x, y) or p (x, y, z) and so on.
The polynomial’s degree is the highest exponent or power of the variable in the polynomial function.
The polynomials provided are:
[tex]p(x) = 3x^{2}y^{2} + 5xy - x^{6}\\\\q(x) = 3x^{5} - 4x^{3} + 2[/tex]
The degree of polynomial p (x) is:
[tex]\text{deg}\ p (x)=6[/tex]
The degree of polynomial q (x) is:
[tex]\text{deg}\ q (x)=5[/tex]
The difference of the degrees of the polynomials p (x) and q (x) is:
[tex]\text{deg}\ p(x)-\text{deg}\ q(x)=6-5=1[/tex]
Thus, the difference of the degrees of the polynomials p (x) and q (x) is 1.
