Question

onsists of terms that have variables with nonnegative integers as exponents consists of any finite number of terms Based on these properties, write down the general form of a polynomial function and define the degree of a polynomial.

Answer 1

Check Explanation

Explanation:

The general form of a polynomial function is given as

aₙxⁿ + aₙ₋₁xⁿ⁻¹ + aₙ₋₂xⁿ⁻² +.......+ a₀x⁰

aₙ, aₙ₋₁, aₙ₋₂, ......., a₀ are all the coefficients of the terms of the polynomial.

And n, n-1, n-2, ...., 0 correspond to the non-negative integers as exponents.

The degree of a term of a polynomial refers to the sum of the exponents of a term of the polynomial. Because the exponents are non-negative, the degree of each term is non-negative too.

The degree of a polynomial is then defined as the highest degree among the degrees of each of the polynomial's terms. Definitely non-negative too.

In the general formula of a polynomial I provided above, the degree of this polynomial is obviously 'n'. This is because it is the highest degree among the degrees of each term of the polynomial's terms (n, n-1, n-2, ..., 0).

Hope this Helps!!!