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Degree of a Polynomial

Degree of a Polynomial

Degree of a Polynomial

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We continually update the degree of the polynomial in question, the degree will always be a member of the following list: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Its graph can be found in the various places.

Degree

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In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer. For a univariate polynomial, the degree of the polynomial is simply the highest exponent occurring in the polynomial.

Like any constant value, the value 0 can be considered as a (constant) polynomial, called the zero polynomial. It has no nonzero terms, and so, strictly speaking, it has no degree either. As such, its degree is usually undefined. The propositions for the degree of sums and products of polynomials in the above section do not apply, if any of the polynomials involved is the zero polynomial. (Source: en.wikipedia.org)

Polynomial

It can be shown that the degree of a polynomial over a field satisfies all of the requirements of the norm function in the euclidean domain. That is, given two polynomials f(x) and g(x), the degree of the product f(x)g(x) must be larger than both the degrees of f and g individually. In fact, something stronger holds: (Source:

We know that the polynomial can be classified into polynomial with one variable and polynomial with multiple variables (multivariable polynomial). As discussed above, the degree of the polynomial with one variable is the higher power of the polynomial expression. But, if a polynomial has multiple variables, the degree of the polynomial can be found by adding the powers of different variables in any terms present in the polynomial expression. (Source: byjus.com)

 

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