Solving Equations by Factoring

Factoring is a method that can be used to solve equations of degree higher than 1. This method uses the zero product rule.

Example 1: Solve x( x + 3) = 0.

Apply the zero product rule.

Check the solution.

The solution is x = 0 or x = −3.

Example 2: Solve x² − 5 x + 6 = 0.

Factor.

Apply the zero product rule.

The check is left to you. The solution is x = 2 or x = 3.

Example 3: Solve 3 x(2 x − 5) = −4(4 x − 3).

Distribute.

Get all terms on one side, leaving zero on the other, in order to apply the zero product rule.

Factor.

Apply the zero product rule.

The check is left to you. The solution is or .

Example 4: Solve 2 y³ = 162 y.

Get all terms on one side of the equation.

Factor (GCF).

Continue to factor (difference of squares).

Apply the zero product rule.

The check is left to you. The solution is y = 0 or y = −9 or y = 9.

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