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Determine the value of k for which x+2 i...

Determine the value of `k` for which `x+2` is a factor of `(x+1)^7+(2x+k)^3dot`

Text Solution

Verified by Experts

The correct Answer is:
`k = 5`
Let `f(x) = (x + 1)^(7) + (2x + k)^(3)` . Now
`f(-2) = (-2+ 1)^(7)+ (-4 + k)^(3) = 0`
or `(k-4)^(3) - 1 =0`
or ` k = 5`
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