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Answer:
[tex]→12 {x}^{3} + 4 {x}^{2} + 3x + 1 \\ = 4 {x}^{2} (3x + 1) + 1(3x + 1) \\ = \boxed{(3x + 1)(4 {x}^{2} + 1)}✓[/tex]