Hey there!
To find the degree of a polynomial, all you need to do is add up the exponents of each individual term. Remember that if a term doesn't have an exponent, there is an implied 1 for the exponent of that term.
[tex]5a^2bc+6a^2b^3c-7b^2c^7[/tex]
[tex]5a^2b^1c^1+6a^2b^3c^1-7b^2c^7[/tex]
[tex]5a^2b^1c^1 = 2+1+1 = 4[/tex]
[tex]6a^2b^3c^1 = 2+3+1 = 6[/tex]
[tex]-7b^2c^7 = 2+7 = 9[/tex]
The sum of the exponents of a term that is the greatest will be the degree of your polynomial. In this problem, this will be your last term, [tex]-7b^2c^7[/tex], and your degree will be 9.
Hope this helped you out! :-)
