Question : If $x^{3}+2x^{2}-5x+k$ is divisible by $x+1$, then what is the value of $k$?
Option 1: –6
Option 2: –1
Option 3: 0
Option 4: 6
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Correct Answer: –6
Solution :
Given: $f(x)=x^3+2x^2-5x+k=0$ is divisible by $x+1$.
So, $ x^3+2x^2-5x+k=0$ when $x=-1$
⇒ $ (-1)^3+2(-1)^2-5(-1)+k=0$
⇒ $-1+2+5+k=0$
⇒ $ k = -6$
Hence, the correct answer is –6.
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