If (x + 1) is a factor of the polynomial \(x^{3} + px^{2} + x + 6\). Find the value of p.

If (x + 1) is a factor of the polynomial \(x^{3} + px^{2} + x + 6\). Find the value of p.

Answer Details

If (x + 1) is a factor of the polynomial, it means that if we substitute -1 in the polynomial, it should give us zero. Therefore: \((-1)^3 + p(-1)^2 -1 + 6 = 0\) Simplifying the above equation, we get: \(-1 + p + 5 = 0\) \(p = -4\) Hence, the value of p is -4. So the correct answer is.