Factoring a cubic

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I'm doing Calc 1 homework and it strikes me that when you have a cubic $x^3-5x+2$ and you put $-5x+2$ to one side and $x^3$ on the other you're essentially looking for where the graph of $x^3$ intersects with the graph of $-5x+2$. To put it into context the homework is asking us to find zeroes for the equation. Is there any equation that would let one evaluate where $x^3$ and $5x+2$ intersect?

Pardon me if this is kind of dumb. I'm beginning to share the little discoveries I make when I'm doing math and I have no gauge of whether they're worth anything to me or not. Talking about them with a community seems like the only way to truly gain an understanding.

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Hint:

Observe that $2$ is a root of the polynomial. Hence,

$$x^3-5x+2=(x-2)q(x)$$

where $q$ is a quadratic term.

Btw, it should be intersection of $5x-2$ and $x^3$.