Q.

f(x) is a four -degree polynomial and the coefficient of \({x}^{4}\) is 1.

If f(1) = 5, f(2) = 10, f(3) = 15 and f(4) = 20 then, what is the value of f(5) ?

A. 25

B. 30

C. 49

D. 34

E. 36

C. 49

f(x) = c(x-1)(x-2)(x-3)(x-4) + 5x

As leading coefficient = 1 ,c = 1

\(\Rightarrow\) f(x) = (x-1)(x-2)(x-3)(x-4) + 5x

\(\Rightarrow\) f(5) = 4×3×2×1 + 5×5

= 49