EQUATION SOLVING: Solve the equation.

Question

x³ − 3x² − 4x + 12 = 0

Answer 1

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

possible solutions are ± all factors of 12 (p/q where p=factors of constant 12 and q=factors of coefficient 1 of x^3)

-1,1,-2,2,-3,3,-4,4,-6,6,-12,12

by trial and error 2 is a solution

divide x^3-3x^2-4x+12 by x-2 to get x^2-x-6

x^2-x-6=0

factor

(x-3)(x+2)=0

x-3=0, x=3

x+2=0, x=-2

the solutions are x=-2, x=2, and x=3

another way to solve is by factoring

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

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

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

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

x-3=0 and x^2-4=0

x=3 and (x-2)(x+2)=0

x=3 and x=2 and x=-2