You have the following polynomial given in the exercise:
[tex]-2xy^5+3x^7-10x^3y^6+8x^6+4[/tex]As you can see, terms of a polynomial are separated by these signs:
[tex]\begin{gathered} + \\ - \end{gathered}[/tex]Therefore, this polynomial has five terms.
In order to find the degree of the polynomial, since it has two variables, you need to add the exponents of both variables of the corresponding term:
For the term
[tex]-2xy^5[/tex]The variable "x" has exponent 1 and the variable "y" has exponent 5. Then:
[tex]-2xy^5\rightarrow1+5=6[/tex]For next terms, you get:
[tex]\begin{gathered} 3x^7\rightarrow7 \\ \\ -10x^3y^6\rightarrow3+6=9 \\ \\ 8x^6\rightarrow6 \end{gathered}[/tex]Notice that the greatest value is 9. Therefore:
[tex]Degree=9[/tex]Notice tha the last term of the polynomial does not multiply any variable. Then, the Constant term is:
[tex]4[/tex]Knowing the sum of the exponents of each term, you can identify that the polynomial is not in decreasing degree order.
The Leading coefficient of a polynomial is the coefficient that multiply the variables with the highest exponents. Then, the Leading coefficient in this case is:
[tex]-10[/tex]The answers are:
First option.
Fourth option.