Equating coefficients
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In mathematics, the method of equating the coefficients is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomial are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas into a desired form.
[edit] Example
Suppose we want to apply partial fraction decomposition to the formula
that is, we want to bring it into the form
in which the unknown parameters are a, b and c. Multiplying these formulas by x(x − 1)(x − 2) turns both into polynomials, which we equate:
or, after expansion and collecting terms with equal powers of x:
At this point it is essential to realize that the polynomial 1 is in fact equal to the polynomial 0x2 + 0x + 1, having zero coefficients for the positive powers of x. Equating the corresponding coefficients now results in this system of linear equations:
Solving it results in:
