EQUATION SOLVING: Solve the equation.

Question

x³ − 3x² − 4x + 12 = 0

Answer 1

Factor by grouping

x³ − 3x² − 4x + 12 = 0

x²(x-3)-4(x-3)=0

(x-3)(x²-4)=0 Factor the difference of squares term

(x-3)(x-2)(x+2) Set each factor equal to zero and solve

x-3=0 Add 3 to both sides

x-3+3=0+3 Simplify

x=3

x-2=0 Add 2 to both sides

x-2+2=0+2 Simplify

x=2

x+2=0 Subtract 2 from both sides

x+2-2=0-2 Simplify

x=-2

x=3,2,-2