9x4 + x2 + x7 - 12

list the degree of each term; 

9x4 is the first term.  Its degree is 4 because that's its exponent of the
variable x.

x2 is the second term.  Its degree is 2 because that's its exponent of the
variable x.

x7 is the third term. Its degree is 7 because that's its exponent of the
variable x.

-12 is the fourth term. Its degree is 0 because, since x0 = 1 and -12
therefore equals to -12x0, -12 has an understoon exponent of the variable x.

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(b) determine the leading term and the leading coefficient;

The leading term is the one which has the largest exponent of the variable x.
This is the third term x7.  The leading coefficient is the coefficient of the
leading term.  Therefore the leading coefficient is the understood 1
coefficient of the leading term x7.

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(c) determine the degree of the polynomial.

The degree of a polynomial is the same as the degree of its leading term.
Therefore the degree of the entire polynomial is the same as the degree of
the leading term x7, which is 7.

Edwin