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Let y (x)= ax3 + bx2 + cx + d
y(0) = 1

0 + 0 + 0 + d=1,

So d = 1
y(1) = 0

a + b + c + 1=0

a + b + c = -1
y(2) = 1

8a + 4b + 2c + 1=1

8a + 4b + 2c = 0
y(3) = 10

27a + 9b + 3c + 1=10

27a + 9b + 3c = 9 

9a + 3b + c = 3

a + b + c = -1        ..........(1)
8a + 4b + 2c = 0   ...........(2)
9a + 3b + c = 3     ...........(3)

From eqn. 1 and eqn. 3:

a - 9a + b - 3b + c - c = -1 - 3
-8a - 2b = -4
-4a - b = -2
4a + b = 2
eqn. 2 - and eqn.3:

8a - 18a + 4b - 6b + 2c - 2c = 0 - 6
-10a - 2b = -6
-5a - b = -3
5a + b = 3
subtract 5a + b = 3 from 4a + b = 2:
4a - 5a + b - b = 2 - 3
-a = -1

a = 1
substitute a = 1 into 4a + b = 2:
4 + b = 2 --> b = -2
subsitute a = 1 and b = -2 into a + b + c = -1:
1 - 2 + c = -1
-1 + c = -1
c = 0

So cubic polynomial equation is:
y (x)= x3 - 2x2 + 1
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