Search results
Results from the WOW.Com Content Network
Every polynomial with rational coefficients, may be factorized, in a unique way, as the product of a rational number and a polynomial with integer coefficients, which is primitive (that is, the greatest common divisor of the coefficients is 1), and has a positive leading coefficient (coefficient of the term of the highest degree). For example:
C is the correction factor; λ is the mean free path; d is the particle diameter; A n are experimentally determined coefficients. For air (Davies, 1945): [2] A 1 = 1.257 A 2 = 0.400 A 3 = 0.55. The Cunningham correction factor becomes significant when particles become smaller than 15 micrometers, for air at ambient conditions.
Modern algorithms and computers can quickly factor univariate polynomials of degree more than 1000 having coefficients with thousands of digits. [3] For this purpose, even for factoring over the rational numbers and number fields, a fundamental step is a factorization of a polynomial over a finite field.
A polynomial f of degree n greater than one, which is irreducible over F q, defines a field extension of degree n which is isomorphic to the field with q n elements: the elements of this extension are the polynomials of degree lower than n; addition, subtraction and multiplication by an element of F q are those of the polynomials; the product ...
Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is a composite number, or it is not, in which case it is a prime number. For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because it cannot be decomposed in this way.
Factoring out the gcd's from the coefficients, we can write = ′ and = ′ where the gcds of the coefficients of ′, ′ are both 1. Clearly, it is enough to prove the assertion when f , g {\displaystyle f,g} are replaced by f ′ , g ′ {\displaystyle f',g'} ; thus, we assume the gcd's of the coefficients of f , g {\displaystyle f,g} are ...
Drag coefficients in fluids with Reynolds number approximately 10 4 [1] [2] Shapes are depicted with the same projected frontal area. In fluid dynamics, the drag coefficient (commonly denoted as: , or ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.
Given a quadratic polynomial of the form + + it is possible to factor out the coefficient a, and then complete the square for the resulting monic polynomial. Example: + + = [+ +] = [(+) +] = (+) + = (+) + This process of factoring out the coefficient a can further be simplified by only factorising it out of the first 2 terms.