Identify the degree of each term of each polynomial. Then find the degree of the polynomial. xy^3 + 7x^3y^2 - 6xy^4 + 2
I am really having trouble with how this process works. I know the degree of the polynomial is 5 but I don't know how to identify the degree of each term. I think the first term is xy^3 is 4. But I am not sure and I can't figure the second term
Whats an equation
add the exponents of all the variables in each term.
The degrees can be easily seen to be
4, 5, 5, 0
The degree of the polynomial is the highest degree among the terms. In this case, 5.
To determine the degree of each term in a polynomial, you need to consider the exponents of the variables in each term. The degree of a term is the sum of the exponents of all the variables in that term.
Let's analyze each term in the given polynomial:
1. Term: xy^3
- Here, we have variables x and y, with exponents 1 and 3.
- The degree of this term is obtained by adding the exponents: 1 + 3 = 4.
2. Term: 7x^3y^2
- This term contains x and y variables with exponents 3 and 2, respectively.
- The degree of this term is also obtained by adding the exponents: 3 + 2 = 5.
3. Term: -6xy^4
- This term has x and y variables with exponents 1 and 4 respectively.
- The degree of this term is 1 + 4 = 5, just like the previous term.
4. Constant term: 2
- A constant term doesn't contain any variables.
- The degree of this term is considered to be 0 because there are no variables involved.
Now, to determine the degree of the polynomial as a whole, you look for the highest degree among all the terms. In this case, the highest degree is 5 (from terms 2 and 3), so the degree of the polynomial is 5.
Therefore, the degree of each term is as follows:
- xy^3: degree 4
- 7x^3y^2: degree 5
- -6xy^4: degree 5
- 2: degree 0