Polynomial identity
= Polynomial identity
{title2=$P(x)=Q(x)$}
A polynomial identity is equality of two <polynomials> for every value of the variables, rather than an equation imposed only at selected roots. Over the real or complex numbers, this is equivalent to equality of corresponding coefficients: their difference, if nonzero, has only finitely many roots in one variable. The <binomial theorem> is an example. Coefficient comparison transfers a polynomial product identity into finite sums of <binomial coefficients>.