The degree of a polynomial is the greatest power of its variables that appear among its terms.
The given polynomial, is:
[tex]5x^4-3x^2+2x^6-x+7[/tex]The powers that appear on the variable x are 4, 2, 6, 1 and 0. The greatest exponent is 6. Therefore, the degree of this polynomial is:
[tex]6[/tex]