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In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...
Animation showing the use of synthetic division to find the quotient of + + + by .Note that there is no term in , so the fourth column from the right contains a zero.. In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division.
Encarta Calculator: Lite version of Microsoft Math 3.0; part of Microsoft Student 2008 Microsoft Mathematics 4.0 (removed): The first freeware version, released in 32-bit and 64-bit editions in January 2011; [ 8 ] features a ribbon GUI
The names for the degrees may be applied to the polynomial or to its terms. For example, the term 2x in x 2 + 2x + 1 is a linear term in a quadratic polynomial. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. Unlike other constant polynomials, its degree is not zero.
The simplest example given by Thimbleby of a possible problem when using an immediate-execution calculator is 4 × (−5). As a written formula the value of this is −20 because the minus sign is intended to indicate a negative number, rather than a subtraction, and this is the way that it would be interpreted by a formula calculator.
A similar problem, involving equating like terms rather than coefficients of like terms, arises if we wish to de-nest the nested radicals + to obtain an equivalent expression not involving a square root of an expression itself involving a square root, we can postulate the existence of rational parameters d, e such that
For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial factorization of x 2 – 4. Factorization is not usually considered meaningful within number systems possessing division , such as the real or complex numbers , since any x {\displaystyle x} can be trivially written as ( x y ) × ( 1 / y ) {\displaystyle ...
In it, geometrical shapes can be made, as well as expressions from the normal graphing calculator, with extra features. [8] In September 2023, Desmos released a beta for a 3D calculator, which added features on top of the 2D calculator, including cross products, partial derivatives and double-variable parametric equations. [9]