p ( x ) = ∑ i = 0 n a i x i , a n ≠ 0 {\displaystyle p(x)=\sum _{i=0}^{n}a_{i}x^{i},a_{n}\neq 0}
p ( x ) = a n x n + ∑ i = 0 n − 1 a i x i {\displaystyle p(x)=a_{n}x^{n}+\sum _{i=0}^{n-1}a_{i}x^{i}}
p ( x − 1 ) = a n ( x − 1 ) n + ∑ i = 0 n − 1 a i ( x − 1 ) i {\displaystyle p(x-1)=a_{n}(x-1)^{n}+\sum _{i=0}^{n-1}a_{i}(x-1)^{i}}
( x − 1 ) n = ∑ k = 0 n ( n k ) x n − k ( − 1 ) k {\displaystyle (x-1)^{n}=\sum _{k=0}^{n}{n \choose k}x^{n-k}(-1)^{k}}
p ( x − 1 ) = a n ∑ k = 0 n ( n k ) x n − k ( − 1 ) k + ∑ i = 0 n − 1 a i ( x − 1 ) i {\displaystyle p(x-1)=a_{n}\sum _{k=0}^{n}{n \choose k}x^{n-k}(-1)^{k}+\sum _{i=0}^{n-1}a_{i}(x-1)^{i}}
p ( x − 1 ) = a n x n + a n ∑ k = 1 n ( n k ) x n − k ( − 1 ) k + ∑ i = 0 n − 1 a i ( x − 1 ) i {\displaystyle p(x-1)=a_{n}x^{n}+a_{n}\sum _{k=1}^{n}{n \choose k}x^{n-k}(-1)^{k}+\sum _{i=0}^{n-1}a_{i}(x-1)^{i}}