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Find the value of 'k' if x+3, is a facto...

Find the value of 'k' if x+3, is a factor of the polynomial `x^(4)-x^(3)-11x^(2)-x+k`.

A

`k=-13`

B

`k=-12`

C

`k=-14`

D

`k=-15`

Text Solution

Verified by Experts

The correct Answer is:
B
Let x+3=0
`implies x=-3`
Let `p(x)=x^(4)-x^(3)-11x^(2)-x+k`
`because x+3`, is a factor of p(x)
`therefore p(-3)=0`
`implies (-3)^(4)-(-3)^(3)-11(-3)^(2)-(-3)=k=0`
`implies 81+27-99+3+k=0`
`implies 12+k=0`
`implies k=-12`
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