If (x + 1) is a factor of the polynomial \(x^{3} + px^{2} + x + 6\). Find the value of p.
- -8
-
-4
- 4
- 8
The correct answer is: B
Explanation
If (x + 1) is a factor, then f(-1) = 0.
\((-1)^{3} + p(-1)^{2} + (-1) + 6 = 0\)
\(-1 + p - 1 + 6 = 0 \implies p + 4 = 0\)
\(p = -4\)