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

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(35256) (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.

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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

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Answer:

So the solution set is

Notice if we graph , we can visually verify our answer.

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