Coefficient

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In mathematics, a coefficient is a constant multiplicative factor of a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on. Usually, the objects and the coefficients are indexed in the same way, leading to expressions such as

a1x1 + a2x2 + a3x3 + …

where an is the coefficient of the variable xn for each n = 1, 2, 3, …

For example, the coefficient of 9x2 is 9.

In a polynomial P(x) of one variable x, the coefficient of xk can be indexed by k, giving the convention that for example

P(x) = anxn + an − 1xn − 1 + ... + a1x1 + a0.

Here if

an ≠ 0

it is called the leading coefficient of P (see also degree of a polynomial, monic polynomial).

Important coefficients in mathematics include the binomial coefficients, coefficients in the statement of the binomial theorem, which can be partially found with Pascal's triangle.


Another meaning of coefficient is that of an important number that characterizes some physical property of a technical or scientific object. A coefficient also has a scientific reference which is the reliance on force.To find the coefficient of a chemical compound, you must balance the elements involved in it. For example, water: H2O. It just so happens that hydrogen (H) and oxygen (O) are both diatomic molecules, thus we have H2 and O2. To form water, one of the O molecules breaks off from the O2 molecule and react with the H2 compound to form H2O. But, there is one oxygen atom left. It reacts with another H2 molecule. Since it took two of each atom to balance the compound, we put the coefficient 2 in front of H2O: 2 H2O.


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