Question

What is the degree of the polynomial a4 + b3 - 2ab + c?

Answer 1

The degree of any given polynomial is said to be the highest power in the exponent of variables given in the polynomial.

For example, quadratic equations like (4x² + 4x + 1) have degree 2.

Here given polynomial is (a⁴ + b³ - 2a·b + c), this polynomial is a multivariable expression.

It is clearly visible that the highest power in the exponent of its variables is 4.

So, the degree of the given polynomial is 4.

Answer 2

For this case we have a polynomial of two variables.
 The variables of the polynomial are:
 variable 1: a
 variable 2: b
 The degree of the polynomial, in this case, is given by the term of the polynomial that has the highest exponent.
 We then have the following polynomial:
 $a ^ 4 + b ^ 3 - 2ab + c$
 The term with the greatest exponent is:
 $a ^ 4$
 Therefore, the polynomial is of degree 4.
 Answer:
 The polynomial is of degree 4.