x^3+3x^2+4x+12=0

Question

Factor to solve for x.

Answer 1

x^3 + 3x^2 + 4x +12 = 0

factor by grouping

1st two terms one group, and last 2 terms the other group

(x^3+3x^2) + (4x+12) = 0

x^2(x+3) +4(x+3) = 0

(x^2+4)(x+3) = 0

set each factor = 0 and solve for x

x^2+4=0, x^2=-4, x=2i,-2i

x+3 = 0, x=-3

x =-3,-2i,2i

Answer 2

x²(x + 3) + 4(x + 3) = (x + 3)(x² + 4) = 0; x + 3 = 0; x = - 3; or x² + 4 = 0; x = 2i.

Answer: {-3, 2i, - 2i}