1. ## 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?

2. Originally Posted by booper563
2 questions.

Explain how you could use a graph to solve inequality x^3-2x^2>4x-8.
graph $\displaystyle f(x) = x^3 - 2x^2$ and $\displaystyle g(x) = 4x - 8$. the interval(s) on which $\displaystyle f(x) > g(x)$ is your solution.

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

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

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

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

can you finish?