Solving Cubic Equations by Factoring
In the next example there are more than two factors, but we can still write an
equivalent equation by setting each factor equal to 0.
Example 1
Solving a cubic equation by factoring
Solve 2x^{3}  3x^{2}  8x + 12 = 0.
Solution
First notice that the first two terms have the common factor x^{2} and the last two terms
have the common factor 4.
x^{2}(2x 
3)  4(2x  3) = 0 
Factor by grouping. 
(x^{2} 
4)(2x  3)= 0 
Factor out 2x  3. 
(x  2)(x + 2)(2x 
3) = 0 
Factor completely. 
x  2 = 0 
or 
x + 2 = 0 
or 
2x  3 = 0 
Set each factor equal to 0. 
x = 2 
or 
x = 2 
or 


The solution set is
. Check each solution in the original equation.
