Answer
NOT a factor
Work Step by Step
Equating the factor, $ x+1 ,$ to zero and then solving for $x,$ then \begin{align*} x+1&=0 \\ x&=-1 .\end{align*} Substituting $x= -1 $ in the given expression, $ x^3+4x^2+x-6 ,$ results to \begin{align*} & (-1)^3+4(-1)^2+(-1)-6 \\&= -1+4(1)-1-6 \\&= -1+4-1-6 \\&= -4 .\end{align*} Since the substitution above is NOT equal to zero, then the remainder is NOT zero. By the Factor Theorem, $ x+1 $ is not a factor of $x^3+4x^2+x-6$.
