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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# 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 2x3 - 3x2 - 8x + 12 = 0.

Solution

First notice that the first two terms have the common factor x2 and the last two terms have the common factor -4.

 x2(2x - 3) - 4(2x - 3) = 0 Factor by grouping. (x2 - 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.

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