If x3 + 2x2 – 5x + k is divisible by x + 1, then what is the value of k?

Using remainder theorem the given expression should be equal to zero when we

put x + 1 = 0, Or x = -1

⇒ x3 + 2x2 – 5x + k = 0 when x = -1

⇒ -13 + 2(-1)2 – 5 (-1) + k = 0

⇒ k = -6

∴ the value of k is - 6