When are these quadratic inequalities true together?

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The inequalities \(x^2 + 3x + 2 > 0\) and \(x^2 + x < 2\) are met by all \(x\) in the region:

1. \(x < -2\);

2. \(-1 < x < 1\);

3. \(x > -1\);

4. \(x > -2\).

Can we write the quadratic expressions in a more useful form?

What would the inequalities look like on a graph?