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In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
Ficus carica is a gynodioecious, deciduous tree or large shrub that grows up to 7–10 m (23–33 ft) tall, with smooth white bark. Its fragrant leaves are 12–25 cm ( –10 in) long and 10–18 cm (4–7 in) wide, and are deeply lobed (three or five lobes).
Figs and fig wasps have had a symbiotic relationship throughout history. [8] The fig wasps need the figs in order to reproduce, while the figs rely on the wasps to aid them in their pollination. [9] In wilder forms of the plant, without pollination the young developing fig will fall off of the tree without ripening.
Therefore, let f(x) = g(x) = 2x + 1. Then, f(x)g(x) = 4x 2 + 4x + 1 = 1. Thus deg(f⋅g) = 0 which is not greater than the degrees of f and g (which each had degree 1). Since the norm function is not defined for the zero element of the ring, we consider the degree of the polynomial f(x) = 0 to also be undefined so that it follows the rules of a ...
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Monic polynomial. In algebra, a monic polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1. That is to say, a monic polynomial is one that can be written as [ 1] with.
The binomial approximation is useful for approximately calculating powers of sums of 1 and a small number x. It states that. It is valid when and where and may be real or complex numbers . The benefit of this approximation is that is converted from an exponent to a multiplicative factor. This can greatly simplify mathematical expressions (as in ...
Irreducible polynomial. In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility depends on the nature of the coefficients that are accepted for the possible factors, that is, the ring to which the coefficients of the ...
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