If x 3+ 2x 2– 5x + k is divisible by x + 1, then what is the value of k?
–6
By the Factor Theorem, if \(x+1\) divides \(P(x)=x^{3}+2x^{2}-5x+k\), then \(P(-1)=0\).
\[P(-1)=(-1)^{3}+2(-1)^{2}-5(-1)+k=-1+2+5+k=6+k\]
Setting \(6+k=0\) gives \(k=\mathbf{-6}\).
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