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PARI/GP is a computer algebra system that facilitates number-theory computation. Besides support of factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials, power series, algebraic numbers, and transcendental functions. [3]
Microsoft Math Solver (formerly Microsoft Mathematics and Microsoft Math) is an entry-level educational app that solves math and science problems. Developed and maintained by Microsoft , it is primarily targeted at students as a learning tool.
The theorem is a special case of the polynomial remainder theorem. [1] [2] The theorem results from basic properties of addition and multiplication. It follows that the theorem holds also when the coefficients and the element belong to any commutative ring, and not just a field.
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 ...
Bolzano's theorem (real analysis, calculus) Bolzano–Weierstrass theorem (real analysis, calculus) Bombieri's theorem (number theory) Bombieri–Friedlander–Iwaniec theorem (number theory) Bondareva–Shapley theorem ; Bondy's theorem (graph theory, combinatorics) Bondy–Chvátal theorem (graph theory) Bonnet theorem (differential geometry)
For example, () = = is the number of different podiums—assignments of gold, silver, and bronze medals—possible in an eight-person race. On the other hand, x ( n ) {\displaystyle x^{(n)}} is "the number of ways to arrange n {\displaystyle n} flags on x {\displaystyle x} flagpoles", [ 8 ] where all flags must be used and each flagpole can ...
Another example is the fundamental theorem of calculus [8] (and its vector versions including Green's theorem and Stokes' theorem). The opposite of deep is trivial . A trivial theorem may be a result that can be derived in an obvious and straightforward way from other known results, or which applies only to a specific set of particular objects ...
For example, to factor =, the first try for a is the square root of 5959 rounded up to the next integer, which is 78. Then b 2 = 78 2 − 5959 = 125 {\displaystyle b^{2}=78^{2}-5959=125} . Since 125 is not a square, a second try is made by increasing the value of a by 1.