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A Coefficient is a multiplicative factor in a mathematical expression.




  • (Wikipedia, 2015) ⇒ Retrieved:2015-11-7.
    • In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but in any case does not involve any variables of the expression. For instance in : [math]\displaystyle{ 7x^2-3xy+1.5+y }[/math] the first two terms respectively have the coefficients 7 and −3. The third term 1.5 is a constant. The final term does not have any explicitly written coefficient, but is considered to have coefficient 1, since multiplying by that factor would not change the term. Often coefficients are numbers as in this example, although they could be parameters of the problem, as a, b, and c, where "c" is a constant, in : [math]\displaystyle{ ax^2+bx+c }[/math] when it is understood that these are not considered variables.

      Thus a polynomial in one variable x can be written as : [math]\displaystyle{ a_k x^k + \dotsb + a_1 x^1 + a_0 }[/math] for some integer [math]\displaystyle{ k }[/math] , where [math]\displaystyle{ a_k, \dotsc, a_1, a_0 }[/math] are coefficients; to allow this kind of expression in all cases one must allow introducing terms with 0 as coefficient.

      For the largest [math]\displaystyle{ i }[/math] with [math]\displaystyle{ a_i \ne 0 }[/math] (if any), [math]\displaystyle{ a_i }[/math] is called the leading coefficient of the polynomial. So for example the leading coefficient of the polynomial : [math]\displaystyle{ \, 4x^5 + x^3 + 2x^2 }[/math] is 4.

      Specific coefficients arise in mathematical identities, such as the binomial theorem which involves binomial coefficients; these particular coefficients are tabulated in Pascal's triangle.