Correct Answer: Option C

Explanation

F(x) = Q x D + R
Kx³ + x² - 5x – 2 = Q(2x+1)+R
If 2x+1 = 0 implies x = -¹/₂
∴k(-¹/₂)³ + (-¹/₂)² -5(-¹/₂) -2
= Q(2(-¹/₂) + 1) +2
K(-¹/₈) + ¹/₄ + ⁵/₂ - 2 = Q(-1+1)+2
-^k/₈ + ¹/₄ + ⁵/₂ - 2 = 0+2
(-k+2+20-16) / 8 = 2
(-k+6) / 8 = 2
-k+6 = 2*8
-k+6 = 16
-k = 16-6
-k = 10
∴k = -10

There is an explanation video available below.

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