Why do I love Polynomials so much?

Algebra Level 5

\(ax^{4}+bx^{2}+cx+d\) is a quartic polynomial

such that \((a,b,c,d)\epsilon N\)

Gives,

\(f(1)+f(2)=44\)

\(f(2)+f(3)=146\)

\(f(3)+f(4)=416\)

\(f(5)=694\)

Then evaluate ,

\({f(30)-f(20)}+(\sum a,b,c,d).(\prod a,b,c,d)\)

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