You need to sketch the graph of cubic polynomial `f(x) = 2x^3 + 3x^2 - 17x - 30` such that:

Notice that the curve intersects x axis at `x = -2.5, x = -2` and x`= 3` , hence, the polynomial has 3 real roots `x = -2.5, x = -2` and `x = 3` .

You need to consider only the negaive values of the cubic function, hence, you need to verify where the curve goes below x axis such that:

`x in (-oo,-2.5) => 2x^3 + 3x^2 - 17x - 30 < 0`

`x in (-2,3) => 2x^3 + 3x^2 - 17x - 30 < 0`

**Hence, the function takes negative values, `2x^3 + 3x^2 - 17x - 30 < 0` , if `x in (-oo,-2.5)U(-2,3).` **

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