<p>If \( x+1 \) is a factor of \( f(x) = x^3 + kx^2 - 3x + k + 2 \), then the value of \( k \) is:</p>
Step-by-Step Solution
Key Concept: If (x+1) is a factor of f(x), then f(-1) = 0 by the Factor Theorem. Substitute x = -1 into the polynomial and solve for k.
<p><strong>Step 1:</strong> Apply Factor Theorem: If (x+1) is a factor of f(x), then f(-1) = 0</p><p><strong>Step 2:</strong> Substitute x = -1 into f(x) = x³ + kx² - 3x + k + 2:</p><p>f(-1) = (-1)³ + k(-1)² - 3(-1) + k + 2</p><p>f(-1) = -1 + k + 3 + k + 2</p><p>f(-1) = 2k + 4</p><p><strong>Step 3:</strong> Set f(-1) = 0:</p><p>2k + 4 = 0</p><p>2k = -4</p><p>k = -2</p><p>∴ Answer: B (k = -2)</p>
Correct Answer: B