Find the function fx ax3 bx2 cx d for which f 3 106 f 1

Find the function f(x) = ax^3 + bx^2 + cx + d for which f(- 3) = -106. f(- 1)= - 4. f(1) = 2. and f(2) = 14. f(x) = (Simplify your answer.)

f(x) = ax^3+bx^2 +cx +d

f(-3) = -106

-106 = -27a +9b -3c +d ----(1)

f(-1)

-4 = -a +b -c +d -----(2)

f(1) =2

2 = a+b +c +d ------(3)

f(2) = 14

14 = 8a +4b +2c +d ---(4)

solve the four quations to get the variables: a, b,c, d

solution we get : a=3 b= -3 c= 0 d= 2

So, f(x) = 3x^3 +9x^2 +2