Question 724439
You only list one polynomial, but I guess you just want to see how to do the work through one example.
The expression {{{2a^5-8+6a^7}}} is a polynomial.
Polynomials are made of terms added together.
In this case, {{{2a^5}}} , {{{-8}}} and {{{6a^7}}} are the terms of your polynomial.
Each term has a number, called the coefficient, and may have one or more variables, with or without exponents.
Your polynomial has only one variable, {{{a}}}.

DEGREE:
Each term has a degree, which is the sum of the exponents on the variables. Of course, if there is only one variable, there is just one exponent per term, and you do not need to add.
The degree of term {{{2a^5}}} is {{{highlight(5)}}},
the degree of {{{6a^7}}} is {{{highlight(7)}}}, and
the degree of {{{-8}}} is {{{highlight(0)}}}.
The reason I say the degree of {{{-8}}} is zero is that {{{a^0=1}}},
so {{{-8=-8a^0}}}.
The degree of the polynomial is the degree of the term of highest degree.
So the degree of your polynomial is {{{highlight(7)}}} .
 
FIRST TERM:
Polynomials are written starting with the term of highest degree, continuing with the term of next highest degree, and so on. Even very disorganized people, immediately reorganize terms that way when given a jumbled polynomial.
However, I am guessing that if you are asked for the degree of the first term in {{{2a^5-8+6a^7}}} what's expected is the degree of {{{2a^5}}} , the first term in the polynomial as given to you, before you had a chance to re-arrange the terms.
The same would go for "second term" and "third term."
 
LEADING TERM and LEADING COEFFICIENT:
As polynomials must be written in order of decreasing degree as soon as possible, the leading term is the term of highest degree. And the leading coefficient is the coefficient of the leading term, always written first, in front of the varaiable, leading the whole parade of terms.
So your leading term is {{{6a^7}}} and your leading coefficient is {{{6}}}