f() is a three degree polynomial such that f(1) =1, f(2) =2, f(3)= 3, f(4) =12 then find f(0) = ?

let the polynomial be ax³ +bx² + cx + d .  Then f(0) = d.  

To find the value of d,  solve the equations

f(1) = a + b + c + d =1

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

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

f(4) = 64a + 16b + 4c + d = 12

By solving above equations, you can get a,b,c,d. But, be clever. x², x³, x  will be zero for f(0). So, you have to calculate only d as said by RAJYALAXMI. I cannot find the way to write matrices here. Sorry for that. Solving by cramer’s rule, d = -8.