Solve for x, x є R using algebraic methods. Use a table to show your results.
x^3 – 2x^2 – x + 2 > 0
factor by grouping ...
$\displaystyle x^3 - 2x^2 - x + 2 > 0$
$\displaystyle x^2(x - 2) - (x - 2) > 0$
$\displaystyle (x - 2)(x^2 - 1) > 0$
$\displaystyle (x - 2)(x - 1)(x + 1) > 0$
critical values are $\displaystyle x = 2$ , $\displaystyle x = 1$, and $\displaystyle x = -1$
check each interval between the critical values to determine which interval(s) make the inequality true.