SOLUTION: find the degree of the polynomial w^3x^4 +3+3x^2 u^3 w-2u^6

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Question 1204145: find the degree of the polynomial
w^3x^4 +3+3x^2 u^3 w-2u^6
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

w%5E3%2Ax%5E4+%2B3%2B3x%5E2%2Au%5E3%2A+w-2u%5E6
the degree of the polynomial: 7

highest-degree term: w%5E3%2Ax%5E4

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

If the polynomial has a single variable, then the degree is the largest exponent.

Example: degree of x^3+x^6-12 is 6


If the polynomial has more than one variable, then we add the exponents for each monomial term and look for the largest sum to get the degree.

In the case of w^3x^4 +3+3x^2 u^3 w-2u^6, we have these terms:
w^3x^4
3
3x^2u^3w
-2u^6

The first term has the exponents sum to 3+4 = 7
The second term has the exponents sum to zero. Think of 3 as 3x^0
The third term has its exponents add to 2+3+1 = 6
The fourth term has an exponent sum of 6

We see that the first monomial has the largest exponent sum.
Therefore the degree of w^3x^4+3+3x^2u^3w-2u^6 is 7.