Question

what is the degree of this polynomial 5a^2bc+6a^2b^3c-7b^2c^7

Answer 1

a polynomial is made up of many monomials

the degree of the polynomial is the degree of the monomial with the highest degree

erm, does that make sense? :)

Answer 2

for example, the polynomial can be split in to the following monomials

5a^2bc
6a^2b^3c
7b^2c^7

and we need to find the degree of each of the monomials since they aren't listed in ascending or descending powers

for example, the degree of 5a^2bc is
2 + 1 + 1, which is 4
we cound the powers of the variables, not the numbers when doing the degree
a has a power of 2, b and c have a power of 1.
remember anything to the power of 1 is the same thing

can you find the degree of the other two monomial?

and whichever monomial has the highest degree, that will be the degree of the polynomial