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In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial ...
The non-real factors come in pairs which when multiplied give quadratic polynomials with real coefficients. Since every polynomial with complex coefficients can be factored into 1st-degree factors (that is one way of stating the fundamental theorem of algebra ), it follows that every polynomial with real coefficients can be factored into ...
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations).For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange.
If two or more factors of a polynomial are identical, then the polynomial is a multiple of the square of this factor. The multiple factor is also a factor of the polynomial's derivative (with respect to any of the variables, if several). For univariate polynomials, multiple factors are equivalent to multiple roots (over a suitable extension field).
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
Each pair (GX, ε X) is a terminal morphism from F to X in C; Each pair (FY, η Y) is an initial morphism from Y to G in D; In particular, the equations above allow one to define Φ, ε, and η in terms of any one of the three. However, the adjoint functors F and G alone are in general not sufficient to determine the adjunction. The equivalence ...
This is a list of volume formulas of basic shapes: [4]: 405–406 Cone – , where is the base's radius; Cube – , where is the side's length;; Cuboid – , where , , and are the sides' length;
But if it is used only on the left, it groups two or more simultaneous equations. There are other symbols of grouping. One is the bar above an expression, as in the square root sign in which the bar is a symbol of grouping. For example √ p+q is the square root of the sum. The bar is also a symbol of grouping in repeated decimal digits.
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