Question

Find the degree of the polynomial
2x^4y^2+9x^2y^5-3x^4y^4

Answer 1

Degree 8.

Explanation:

Check each term for the highest degree:

3x^4y^4 has degree 4 + 4 = 8.

The others have degree 6 and 7.

Answer 2

the polynomial has degree 8

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
`2\,x^4\,y^2` contains four variables "x" and two variables "y", so a total of six. Then its degree is: 6

2) term
`9\,x^2\,y^5` contains two variables "x" and five variables "y", so a total of seven. Then its degree is: 7

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

This last term is therefore the leading term of the polynomial (the term with largest degree) and the one that gives the degree to the entire polynomial.