Question

Find the degree of the polynomial
5mn^4+7mn^2p^5+15np

Answer 1

Degree 8.

Explanation:

The term with the highest degree is 7mn^2p^5

It's degree is 1 +2+5 = 8.

The other terms have degree 5 and 2.

Answer 2

The degree of this polynomial is "8"

Explanation:

Recall that the degree of a polynomial is given by the degree of its leading term. 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
`5\,m\,n^4` contains one variable "m" and four variables "n", so a total of five. Then its degree is: 5

2) term
`7\,m\,n^2\,p^5` contains one variable "m", two variables "n", and five variables "p". that is a total of eight variables. Then its degree is: 8

3) term
`15\, n\, p` contains one variable n and one variable p. That is a total of 2. Then its degree is 2.

Based on the analysis above, and the fact that the term with highest degree is that of degree 8, the polynomial has degree 8.