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, x 2 3x10=0

Factor the left side: (x5)(x+2)=0

Set each factor to zero: x5=0orx+2=0

Solve each equation: x=5orx=2

The solution set is { 5,2 } .

Example 2:

Solve the equation, 2 x 2 +5x=12

Set the right side to zero: 2 x 2 +5x12=0

Factor the left side: (2x3)(x+4)=0

Set each factor to zero: 2x3=0 or x+4=0

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

The solution set is { 3 2 ,4 } .