Factor theorem information

In algebra, the factor theorem connects polynomial factors with polynomial roots. Specifically, if f ( x ) {\displaystyle f(x)} is a polynomial, then x...

only if f ( r ) = 0 , {\displaystyle f(r)=0,} a property known as the factor theorem. Let f ( x ) = x 3 − 12 x 2 − 42 {\displaystyle f(x)=x^{3}-12x^{2}-42}...

fundamental theorem of arithmetic, which asserts that every positive integer may be factored into a product of prime numbers, which cannot be further factored into...

The theorem assumes that there are two goods and two factors of production, for example capital and labour. Other key assumptions of the theorem are that...

and q is an integer factor of the leading coefficient an. The rational root theorem is a special case (for a single linear factor) of Gauss's lemma on...

fundamental theorem of algebra, which asserts that every polynomial may be factored into linear factors, one for each root. The theorem, which is named...

regard to input prices such as wages (the state of factor price equalization). The Rybczynski theorem displays how changes in an endowment affects the outputs...

total symmetry factor is 2, and the contribution of this diagram is divided by 2. The symmetry factor theorem gives the symmetry factor for a general diagram:...

mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer...

formulas Integer-valued polynomial Algebraic equation Factor theorem Polynomial remainder theorem See also Theory of equations below. Polynomial ring Greatest...

composition factors, up to permutation and isomorphism. This theorem can be proved using the Schreier refinement theorem. The Jordan–Hölder theorem is also...

In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample...

prime numbers factor into a product of multiple prime ideals in an algebraic number field is addressed by Chebotarev's density theorem, which (when applied...

considering the determinant as univariate in x i , {\displaystyle x_{i},} the factor theorem implies that x j − x i {\displaystyle x_{j}-x_{i}} is a divisor of det...

2-factor theorem (graph theory) 15 and 290 theorems (number theory) 2π theorem (Riemannian geometry) AF+BG theorem (algebraic geometry) ATS theorem (number...

speedup theorem, that the space and time requirements of a Turing machine solving a decision problem can be reduced by a multiplicative constant factor. Blum's...

cancelling the common factor of e(a + b)x from each term gives the ordinary binomial theorem. For the complex numbers the binomial theorem can be combined with...

derived from representations of its two factors, using the Brahmagupta–Fibonacci identity. Jacobi's two-square theorem states The number of representations...

itself can be viewed as the polynomial remainder theorem (the little Bézout theorem, or factor theorem), generalized to an appropriate class of functions...