Find all solutions.
-$$x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0$$
A) $\{ 1 , - 2,2 \}$
B) $\{ 4 \}$
C) $\{ - 1,1 , - 2 \}$
D) $\{ - 2,2 \}$

Question

Quizplus · Accepted Answer

To find all solutions to the cubic equation $x^3 + 2x^2 - x - 2 = 0$, we can attempt to factor it. Factoring by grouping, we get:$$x^2(x + 2) - 1(x + 2) = 0$$$$ (x^2 - 1)(x + 2) = 0$$$$ (x + 1)(x - 1)(x + 2) = 0$$Setting each factor equal to zero gives the solutions $x = -1$, $x = 1$, and $x = -2$, which corresponds to choice C.

Find All Solutions x3+2x2−x−2=0x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0x3+2x2−x−2=0

Find All Solutions $x ^ { 3 } + 2 x ^ { 2 } - x - 2 = 0$