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The cubic polynomial $y(x)$ which takes the following values: $y(0)=1, y(1)=0, y(2)=1$ and $y(3)=10$ is

1. $x^3 +2x^2 +1$
2. $x^3 +3x^2 -1$
3. $x^3 +1$
4. $x^3 -2x^2 +1$
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Ans D)

y(x)=x3-2x2+1

Now, putting x=0 we get y(x)=0-0+1=1

Similarly x=1 we get y(x)=0

x=2 then y=1

x=3 then y=10

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Option D: x^3 - 2 x^2 +1
=x^2(x-2) +1

Now put x values
you'll get answer as option D

(PS: key point here is solve these type of questions using this technique, take common power of x and then solve)
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