Binomial coefficient
Binomial coefficients as a basis for the space of polynomials

Over any field of characteristic 0 (that is, any field that contains the rational numbers), each polynomial p (t) of degree at most d is uniquely expressible as a linear combination ∑ k = 0 d a k (t k) {\textstyle \sum _{k=0}^{d}a_{k}{\binom {t}{k}}} of binomial coefficients, because the binomial coefficients consist of one polynomial of each degree. The coefficient a is the k th difference of the sequence p (0), p (1),..., p (k). Explicitly,
detectable_content:number_placeholders[6], language:response_language[Portuguese]