A polynomial f(x)\equal{}ax^4\plus{}bx^3\plus{}cx^2\plus{}dx with a,b,c,d>0 is such that f(x) is an integer for x \in \{ \minus{}2,\minus{}1,0,1,2 \} and f(1)\equal{}1 and f(5)\equal{}70.
(a) Show that a\equal{}\frac{1}{24}, b\equal{}\frac{1}{4},c\equal{}\frac{11}{24},d\equal{}\frac{1}{4}.
(b) Prove that f(x) is an integer for all xāZ. algebrapolynomialinductionbinomial theoremalgebra unsolved