If f (x) = x^3 + ax + b is divisible by ...

If f (x) = `x^3 + ax + b` is divisible by `(x - 1)^2`, then the remainder obtained when f (x) is divided by (x + 2) is:

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`f(x)=x^3+ax+b=(x-1)^2(x+c)`
`x^3+ax+b=(x^2-2x+1)(x+c)`
`x^3+ax+b=x^3-2x^2+x+x^2-2cx+c)`
`ax+b=(c-2)x^2+(1-2c)x+c`
c-2=0,c=2
`f(-2)=(-2-1)^2(-2+2)=0`

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