Explanation:
The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^3 + 2x^2 - 5x + 1, the term with the highest exponent is 4x^3, which has a degree of 3.
In the case of a polynomial with more than one variable, the degree is found by looking at each monomial within the polynomial, adding together all the exponents within a monomial, and choosing the largest sum of exponents. For example, in the polynomial 3x^2y^3 + 2xy - 1, the monomial with the highest sum of exponents is 3x^2y^3, which has a degree of 5.
The degree of a polynomial is important because it tells us the number of possible turning points on the graph of the polynomial. It also tells us the highest power of the variable that we need to consider when finding the derivative of the polynomial.
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