Trivial by Induction
If is a monic polynomial of degree 10 such that for , then find the value of
The answer is 3628921.
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1 solution
Let F(x)=f(x)-x² then F(1)=F(2)=....=F(10)=0 then F(x)=(x-1)(x-2)(x-3)....(x-10) f(x)=(x-1)(x-2)(x-3)....(x-10)+x² so f(11)=10x9x8...x1+121=3628921