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If x^2+x+1 is a factor of the polynomi...

If `x^2+x+1` is a factor of the polynomial `3x^3+8x^2+8x+3+5k ,` then the value of `k` is 0 (b) `2/5` (c) `5/2` (d) `-1`

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If `x^2+x+1`is a factor of the polynomial`3x^3+8x^2+8x+3+]5k`
We have,`p(x)=3x^3+8x^2+8x+3+5k`
`3x^3+3x^2+3x+5x^2+5x+3+5k`
`p(x)=3x(x2+x+1)+5x2+5x+3+5k`
`p(x)=3x(x^2+x+1)+5x^2+5x+5+5k−2`
`p(x)=3x(x^2+x+1)+5(x^2+x+1)+5k−2`
`(x^2+x+1)(3x+5)+5k−2`Hence remainder `5k-2`
`5k-2=0, k=2/5`
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