To show that \((x + 1)\) is a factor of \(4x^3 - x^2 - 11x - 6\), we can use the Factor Theorem. According to the theorem, \((x + 1)\) is a factor if substituting \(x = -1\) into the polynomial results in zero.

Substitute \(x = -1\) into the polynomial:

\(4(-1)^3 - (-1)^2 - 11(-1) - 6\)

\(= 4(-1) - 1 + 11 - 6\)

\(= -4 - 1 + 11 - 6\)

\(= 0\)

Since the result is zero, \((x + 1)\) is a factor of \(4x^3 - x^2 - 11x - 6\).