Solving Quadratics
Solving Quadratics by Factoring
Once a quadratic equation is factored and set equal to zero, each factor can be used to find a solution, also called a root.
The zero product property
If two expressions multiply to zero, at least one of them must equal zero. Therefore, if (x + 3)(x − 1) = 0, then x + 3 = 0 or x − 1 = 0.
How to solve by factoring
- Move every term to one side so the other side is zero.
- Factor the quadratic completely.
- Set each factor equal to zero.
- Solve the resulting linear equations.
- Substitute the roots to check them.
Worked example
Solve x² − 5x + 6 = 0
- Factor: (x − 2)(x − 3) = 0
- x − 2 = 0 gives x = 2.
- x − 3 = 0 gives x = 3.
The solutions are x = 2 and x = 3.
Common mistakes
- Using the zero product property before setting the equation equal to zero.
- Finding the factors but not solving each factor.
- Changing a sign incorrectly when finding a root.
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