The value of λ for which the expression x3 + x2

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The value of λ for which the expression x³ + x² – 5x + λ will be divisible by (x – 2) is :

1. 2
2. –2z
3. –3
4. 4

Correct Option: B

(x – 2) is a factor of polynomial P (x) = x³ + x² – 5x + λ.
∴ P(2) = 0 (on putting x = 2)
⇒ 2³ + 2² – 5 × 2 + λ = 0
⇒ 8 + 4 – 10 + λ = 0
⇒ λ + 2 = 0
∴ λ = - 2