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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 ...
Cubic equation. Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis at y = 0 ). The case shown has two critical points. Here the function is and therefore the three real roots are 2, -1 and -4. In algebra, a cubic equation in one variable is an equation of the form in which a is not zero.
Monomial order. In mathematics, a monomial order (sometimes called a term order or an admissible order) is a total order on the set of all ( monic) monomials in a given polynomial ring, satisfying the property of respecting multiplication, i.e., If and is any other monomial, then . Monomial orderings are most commonly used with Gröbner bases ...
The graph of a degree 1 polynomial (or linear function) f(x) = a0 + a1x, where a1 ≠ 0, is an oblique line with y-intercept a0 and slope a1 . The graph of a degree 2 polynomial. f(x) = a0 + a1x + a2x2, where a2 ≠ 0. is a parabola . The graph of a degree 3 polynomial. f(x) = a0 + a1x + a2x2 + a3x3, where a3 ≠ 0.
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modeled as an n th degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E ( y | x ).
The theorem. The Sturm chain or Sturm sequence of a univariate polynomial P(x) with real coefficients is the sequence of polynomials such that. for i ≥ 1, where P' is the derivative of P, and is the remainder of the Euclidean division of by The length of the Sturm sequence is at most the degree of P . The number of sign variations at ξ of ...
v. t. e. In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function, the Taylor polynomial is the truncation at the order of the Taylor series of the function.
In mathematics, the order of a polynomial may refer to: the degree of a polynomial, that is, the largest exponent (for a univariate polynomial) or the largest sum of exponents (for a multivariate polynomial) in any of its monomials; the multiplicative order, that is, the number of times the polynomial is divisible by some value; the order of ...