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For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x ...
A polynomial expression is an expression ... root-finding algorithms may be used to find numerical approximations of the roots of a polynomial expression of any degree.
The partial sum formed by the first n + 1 terms of a Taylor series is a polynomial of degree n that is called the n th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally more accurate as n increases.
The largest zero of this polynomial which corresponds to the second largest zero of the original polynomial is found at 3 and is circled in red. The degree 5 polynomial is now divided by () to obtain = + + which is shown in yellow. The zero for this polynomial is found at 2 again using Newton's method and is circled in yellow.
The resulting polynomial is not a linear function of the coordinates (its degree can be higher than 1), but it is a linear function of the fitted data values. The determinant, permanent and other immanants of a matrix are homogeneous multilinear polynomials in the elements of the matrix (and also multilinear forms in the rows or columns).
The degree of a monomial is defined as the sum of all the exponents of the variables, including the implicit exponents of 1 for the variables which appear without exponent; e.g., in the example of the previous section, the degree is + +. The degree of is 1+1+2=4. The degree of a nonzero constant is 0.
A related expression for T n as a sum of monomials with binomial ... as f n (x) is a polynomial of degree n − 1, so the fundamental theorem of algebra implies it ...
the multiplicative order, that is, the number of times the polynomial is divisible by some value; the order of the polynomial considered as a power series, that is, the degree of its non-zero term of lowest degree; or; the order of a spline, either the degree+1 of the polynomials defining the spline or the number of knot points used to ...