User talk:PaoloMartini

$p(x)=\sum _{i=0}^{n}a_{i}x^{i}$

$(x-1)^{n}=\sum _{i=0}^{n}{n \choose i}x^{n-i}(-1)^{i}$

${n \choose k}={n \choose n-k}$

$(x-1)^{n}=\sum _{i=0}^{n}{n \choose i}x^{i}(-1)^{i}$

$p(x-1)=\sum _{i=0}^{n}a_{i}(x-1)^{i}=\sum _{i=0}^{n}(a_{i}\sum _{k=0}^{n}{n \choose k}x^{k}(-1)^{k}).$

$p(x-1)=\sum _{i=0}^{n}a_{i}(x-1)^{i}$

$t=x-1$

$p(t)=\sum _{i=0}^{n}a_{i}t^{i}$