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?
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.
without using graphs, note that the solution here is the same as the solution toAnd
What is the solution to x^3-2x^2>4x-8?
$\displaystyle x^3 - 2x^2 - 4x + 8 > 0$
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?