Solve for x, x є R using algebraic methods. Use a table to show your results.

x^3 – 2x^2 – x + 2 > 0

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- Jul 17th 2009, 09:35 AMwilliamsolving
Solve for x, x є R using algebraic methods. Use a table to show your results.

x^3 – 2x^2 – x + 2 > 0 - Jul 17th 2009, 09:44 AMskeeter
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.