We have to determine the degree of the given polynomial:
[tex]5a^6bc^2+8d^5+7e^6f^2-10g^4h^7[/tex]
For polynomials in more than one variable, the sum of the powers of the variables in each term is taken up and the highest sum so obtained is called the degree of the polynomial.
Since, there are 4 terms in the polynomial.
Consider the first term [tex]5a^6bc^2[/tex],
The sum of powers of variables = 6+1+2 = 9
Consider the second term [tex]8d^5[/tex],
The sum of powers of variables = 5
Consider the third term [tex]7e^6f^2[/tex],
The sum of powers of variables = 6+2 = 8
Consider the fourth term [tex]-10g^4h^7[/tex],
The sum of powers of variables = 4+7 = 11
Since, the highest sum so obtained is 11.
Therefore, the degree of the given polynomial is 11.
