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$Old$ 11-17-2008, 10:35 AM

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$Default$ Inequality x^3-2x^2>4x-8

2 questions.

Explain how you could use a graph to solve inequality x^3-2x^2>4x-8.

And

What is the solution to x^3-2x^2>4x-8?

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$Old$ 11-17-2008, 10:46 AM

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Originally Posted by booper563 $View Post$

2 questions.

Explain how you could use a graph to solve inequality x^3-2x^2>4x-8.

graph $f(x) = x^3 - 2x^2$ and $g(x) = 4x - 8$ . the interval(s) on which $f(x) > g(x)$ is your solution.

or, a harder way: graph $f(x) = x^3 - 2x^2 - 4x + 8$ . the interval(s) on which $f(x) > 0$ is your solution.

Quote:

And

What is the solution to x^3-2x^2>4x-8?

without using graphs, note that the solution here is the same as the solution to

$x^3 - 2x^2 - 4x + 8 > 0$

note further that $x^3 - 2x^2 - 4x + 8 = x^2(x - 2) - 4(x - 2) = (x - 2)(x^2 - 4) = (x + 2)(x - 2)^2$

can you finish?

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