ap algebra

From the graph or table, the solution of the equation is x = -2. To verify this, we can use synthetic division. \begin{align} & \begin{matrix} 6 & 11 & 6 & & 3 \\ 1 &\phantom{-}6 & 22 & 6& \ \ \ \ \frac{6}{-2} \\ & -2 & 20 & & 3 \end{matrix} \\[2ex] & x^3+6x^2+ 11x + 6 = (-2)^3 + 6(-2)^2+ 11(-2) + 6 = 0 \end{align} Therefore, x = -2 is a solution of the equation. To solve the polynomial equation, we can factor the equation as follows. $$x^3+6x^2+ 11x + 6 = (x+2)(x^2+4x+3)$$ The solution set is {-2, -3+i√2, -3-i√2}.