Solving Quadratic Equations Using Factoring

To solve an quadratic equation using factoring:

            1. Transform the equation using standard form in which one side is zero.

            2.  Factor the non-zero side.

            3.  Set each factor to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero).

            4.  Solve each resulting equation.

Example 1:

Solve the equation, x2 – 3x – 10 = 0

Factor the left side: (x – 5)(x + 2) = 0

Set each factor to zero: x – 5 = 0 or x + 2 = 0

Solve each equation: x = 5 or x = –2

The solution set is {5, –2}.

Example 2:

Solve the equation, 2x2 + 5x = 12

Set the right side to zero: 2x2 + 5x – 12 = 0

Factor the left side: (2x – 3)(x + 4) = 0

Set each factor to zero: 2x – 3 = 0 or x + 4 = 0

Solve each equation: x = 3/2 or x = –4

The solution set is {3/2, –4}