Polynomial maths question

Question

f(x)=x⁴+ax³+bx²+cx+d

if f(2)=1, f(3)=2, f(4)=3, f(5)=4 then a+b+c+d= ?

Answer 1

f(2) = 16 + 8a + 4b + 2c + d = 1

f(3) = 81 + 27a + 9b + 3c + d = 2

f(4) =

 

Continue, you shall have four equations in four variables.

Use elimination, Gauss-Jordan, or substitution to solve.