Degree Of A Polynomial
The degree of a polynomial is the highest degree of its terms, when the polynomial is expressed in canonical form (i.e. as a linear combination of monomials). The degree of a term is the sum of the exponents of the variables that appear in it. The word degree is now standard, but in some older books, the word order may be used instead.
For example, the polynomial has three terms. (Notice, this polynomial can also be expressed as .) The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5 which is the highest degree of any term.
To determine the degree of a polynomial that is not in standard form (for example ), one has to put it first in standard form by expanding the products (by distributivity) and combining the like terms; for example, and its degree is 1, although each summand has degree 2. However, this is not needed when the polynomial is expressed as a product of polynomials in standard form, because the degree of a product is the sum of the degrees of the factors.
Read more about Degree Of A Polynomial: Names of Polynomials By Degree, Other Examples, Behavior Under Addition, Subtraction, Multiplication and Function Composition, The Degree of The Zero Polynomial, The Degree Computed From The Function Values, Extension To Polynomials With Two or More Variables, Degree Function in Abstract Algebra
Famous quotes containing the words degree of and/or degree:
“So that if you would form a just judgment of what is of infinite importance to you not to be misled in,—namely, in what degree of real merit you stand ... call in religion and morality.—Look,—What is written in the law of God?—How readest thou?—Consult calm reason and the unchangeable obligations of justice and truth;Mwhat say they?”
—Laurence Sterne (1713–1768)
“Essential truth, the truth of the intellectualists, the truth with no one thinking it, is like the coat that fits tho no one has ever tried it on, like the music that no ear has listened to. It is less real, not more real, than the verified article; and to attribute a superior degree of glory to it seems little more than a piece of perverse abstraction-worship.”
—William James (1842–1910)