2^3 - 4(2) + 2 = 8 - 8 + 2 = 2 \quad (\text{not a root})
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- 1^3 - 4(1) + 2 = 1 - 4 + 2 = -1 \quad (\text{not a root})
- Testing \( x = -1 \):
- Testing \( x = 2 \):
- Testing \( x = -2 \):
- Since none of the rational roots work, we proceed with finding roots using numerical or graphing methods. However, for simplicity, we can use a substitution or derivative analysis to approximate or verify roots.
- Consider \( g(x) = x^3 - 4x + 2 \). The derivative is:
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