Solve for x:
x^3 + 2 x^2 - 11 x - 12 = 0
Factor the left hand side.
The left hand side factors into a product with three terms:
(x - 3) (x + 1) (x + 4) = 0
Find the roots of each term in the product separately.
Split into three equations:
x - 3 = 0 or x + 1 = 0 or x + 4 = 0
Look at the first equation: Solve for x.
Add 3 to both sides:
x = 3 or x + 1 = 0 or x + 4 = 0
Look at the second equation: Solve for x.
Subtract 1 from both sides:
x = 3 or x = -1 or x + 4 = 0
Look at the third equation: Solve for x.
Subtract 4 from both sides:
x = 3 or x = -1 or x = -4
x^3+2x^2-11x-12 = 0 we can write this as
x^3 + x^2 + x^2 - 11x - 12 = 0 factor
x^2(x + 1) + ( x - 12) ( x + 1) = 0
(x + 1) ( x^2 + x - 12) = 0
(x + 1) ( x + 4) ( x - 3) = 0
Setting each factor to 0 and solving for x gives the roots
x = -4, x = -1 and x = 3
And their sum is -2