Quadratic Equation - Factorization

 

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=0x2−3x−10=0

Factor the left side: 

(x−5)(x+2)=0(x−5)(x+2)=0

Set each factor to zero: 

x−5=0  or  x+2=0x−5=0  or  x+2=0

Solve each equation:

 x=5  or  x=−2x=5  or  x=−2

The solution set is {5,−2}{5,−2} .

 

Example 2:

Solve the equation, 2x2+5x=122x2+5x=12

Set the right side to zero: 

2x2+5x−12=02x2+5x−12=0

Factor the left side:

 (2x−3)(x+4)=0(2x−3)(x+4)=0

Set each factor to zero: 

2x−3=02x−3=0 or x+4=0x+4=0

Solve each equation:

 x=32x=32 or x=−4x=−4

The solution set is {32,−4}{32,−4}