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Algebra Level 4

A polynomial of degree 4 and with a leading coefficient of 1 satisfies f(1)=17,f(2)=34,f(3)=51.f\left( 1 \right) =17,\quad f\left( 2 \right) =34,\quad f(3)=51. Determine f(0)+f(4).f(0)+f(4).

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