Factor: 4x^3 + 3x^2 + 12 Factor 4 from the expression: 4(x^3 + (3/4)x^2 + 3) Factor the trinomial: x^3 + (3/4)x^2 + 3 Factor by grouping: (x^2 + 3x) + ((3/4)x^2 + 9) Factor out x from the first group and (3/4) from the second: x(x + 3) + (3/4)(x^2 + 12) Factor the remaining trinomial: x^2 + 12 = (x + 2√3i)(x - 2√3i) Put it all together: 4x^3 + 3x^2 + 12 = 4(x + 3)(x + 2√3i)(x - 2√3i)