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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 3 x 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, 2 x 2 + 5 x = 12

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

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

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

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

The solution set is { 3 2 , 4 } .