Outrageously Funny Word Dictionary :: Irred

👉 Irreducible

irretentive

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👉 Irreducible

irreparability

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👉 In mathematics, a reduction is a process or method used to reduce one mathematical expression into another. It involves identifying and eliminating all instances of variables that are present in both expressions. For example, consider the following two expressions: 1. \(x^2 + y^2\) 2. \(x^3 + y^3\) By reducing these expressions, we can identify that \(x^2\) is a factor of both and can be written as \((x+y)(x-y

irreduction

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👉 In mathematics, an irreducible polynomial is a polynomial that cannot be factored into the product of two non-constant polynomials. This means that every factor of the polynomial must come from the coefficients in some way and can only be obtained by multiplying or dividing it out. For example, consider the polynomial $x^4 - 3x^2 + 1$. It is reducible because it can be factored as $(x^2 - 1)(x^2 -

irreductible

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👉 In mathematics, an algebraic structure is said to be irreducible if it cannot be expressed as a product of simpler structures. This means that any two elements in the structure must have different powers, and no element can be obtained from another by multiplying on both sides of the equation. For example, the set of all positive integers modulo 6 forms an algebraic structure known as the group Z/6Z under addition. It is not possible to express this group as a product of simpler structures like

irreductibility

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👉 The term "irreducibly" is used in mathematics to describe a number or expression that cannot be expressed as a simple fraction with integers. It means that the result of applying any operation (addition, subtraction, multiplication, division) on this number or expression will result in another number or expression that can't be simplified further without changing its value.

irreducibly

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👉 The term "irreducibility" in mathematics refers to a property of polynomials that states that they cannot be factored into two non-constant polynomials, where each polynomial is considered as a factor. This means that if you have a polynomial f(x) = ax^2 + bx + c and g(x) = dx + e, then there are no constants d and e such that f(g(x)) = 0. In other words, the coefficients of f and g must

irreducibleness

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👉 In mathematics, an irreducible polynomial is a polynomial that cannot be factored into linear factors. These polynomials are called irreducible because they have no non-trivial roots (i.e., their coefficients do not contain any other variables). For example: 1. x^2 - 4: This polynomial can be factored as (x + 2)(x - 2), which has two distinct real roots, so it is an irreducible polynomial. 2. x^3 -

irreducible

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👉 In mathematics, an irreducible polynomial is a polynomial that cannot be factored into simpler polynomials. This means that there are no common factors between the coefficients and the variables of the polynomial. For example, x^2 + 1 is not reducible over the real numbers because it can be written as (x+1)(x-1), which has two different factors. Irreducible polynomials are important in algebraic number theory, where they play a crucial role in finding prime

irreducibilities

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👉 In algebra, an irreducible polynomial is a polynomial that cannot be factored into a product of two or more non-constant polynomials. In other words, it has no common factor with any other polynomial in the ring of polynomials over a field. For example, consider the polynomial x^3 - 4x + 1. This polynomial can be factored as (x - 1)(x^2 + x + 1). However, this factorization does not preserve irre

irreducibility

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