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in it in chapter 1 its says

"F(x) = A(x - α1)(x - α2) · · · (x - αr),"

this makes sense to me but then it also said

We next note that the condition f(αk) = 0 for k = 1, 2, . . . , r, could also be met

if (1.8) were replaced by

F(x) = A(x - α1)^m1(x - α2)^m2 · · · (x - αr)^mr

this confused me...how can you can you just raise each factor to powers m1,m2,...mr etc.How does the function still remain same?