Question

Find the degree of the polynomial:
8xyz^7-8x^3yz^4+2x^3y^3

Answer 1

The degree of the polynomial is 9

Explanation:

Recall that the degree of a polynomial is given by the degree of its leading term (the term with largest degree). Recall as well that the degree of a term is the maximum number of variables that appear in it.

So, let's examine each of the terms in the given polynomial, and count the number of variables they contain to find their individual degrees. then pick the one with maximum degree, and that its degree would give the actual degree of the entire polynomial.

1) term
`8\,x\,y\,z^7` contains one variable "x" , one variable "y", and seven variables "z", so a total of nine. Then its degree is: 9

2) term
`-8\,x^3\,y\,z^4` contains three variables "x" , one variable "y", and four variables "z", so a total of eight. Then its degree is: 8

3) term
`2\,x^3\,y^3` contains three variables "x" and three variables "y", so a total of six variables. Then its degree is : 6

Therefore, the leading term of this polynomial is the first one, and it gives its degree to the entire polynomial. the polynomial is of degree 9.