Foundations
Degrees
Multiple Variables
Polynomials and terms can have more than one variable. Here is another example of a polynomial:
The positive integer exponents confirm this example is a polynomial. The polynomial has five terms. Let's look at each term more closely. When a term has multiple variables, the degree of the term is the sum of the exponents within the term.
t4 - 6s3t2 - 12st + 4s4 - 5
The positive integer exponents confirm this example is a polynomial. The polynomial has five terms. Let's look at each term more closely. When a term has multiple variables, the degree of the term is the sum of the exponents within the term.
t4 has a degree of 4, so it's a 4th order term,
-6s3t2 has a degree of 5 (3+2), so it's a 5th order term,
-12st has a degree of 2 (1+1), so it's a 2nd order term,
4s4 has a degree of 4, so it's a 4th order term,
-5 is a constant, so its degree is 0.
Since the largest degree of a term in this polynomial is 5, then this is a polynomial of degree 5 or a 5th order polynomial.