Given a polynomial functin
ax^2+bx+c, the highest degree is 2
given another polynomial say ax^3+bx^2+cx+d, the degree of the polynomial is 3.
From the above we can conclude that the degree of a polynomial is its highest power.
From the function given:
5+7x^9+12x-5x^7+3x^2
The highest power is 9, thus it is a polynomial of degree 9.
The coefficient of the term of degree 9 is 7.
The answer is 7.