# SOLUTION: 2. Solve by graphical means: x^3 – x^2 – 4x + 4 < 0 (Hint: factor by grouping) Label the vertex and axis. Denote the left-hand side by f(x). Factor t

Algebra ->  Algebra  -> Functions -> SOLUTION: 2. Solve by graphical means: x^3 – x^2 – 4x + 4 < 0 (Hint: factor by grouping) Label the vertex and axis. Denote the left-hand side by f(x). Factor t      Log On

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 Algebra: Functions, Domain, NOT graphing Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Functions Question 129111: 2. Solve by graphical means: x^3 – x^2 – 4x + 4 < 0 (Hint: factor by grouping) Label the vertex and axis. Denote the left-hand side by f(x). Factor to find the x intercepts, and sketch the graph with the aid of a few additional points. Answer by jim_thompson5910(28598)   (Show Source): You can put this solution on YOUR website!Let's factor Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms Now factor to get So factors to Notice if we solve we find the zeros , and In order to solve we need to test some points. So let's pick a point that is less than So let's test Start with the given inequality Plug in Simplify. Since this inequality is true, any value that is less than will satisfy the inequality. ---------------------------------- Now let's test a value that is in between and So let's test Start with the given inequality Plug in Simplify. Since this inequality is not true, this means that the interval [-2,1] is not in the solution set. ---------------------------------- Now let's test a value that is in between and So let's test Start with the given inequality Plug in Simplify. Since this inequality is true, any value that is in between x=1 and x=2 will satisfy the inequality. ---------------------------------- Now let's test a value that is greater than So let's test Start with the given inequality Plug in Simplify. Since this inequality is not true, this means that any value greater than x=2 will not satisfy the inequality ----------------------------------------------------------- Answer: So the solution set is Notice if we graph , we can visually verify our answer.