Section 8.3: Solving Quadratic Equations by Factoring

Factoring is a method for solving quadratic equations by expressing them as a product of linear factors and then setting each factor equal to zero.

Standard form: \( ax^2 + bx + c = 0 \)

Example 1

Solve \( x^2 - 5x + 6 = 0 \) by factoring.

Step 1: Factor the quadratic: \( x^2 - 5x + 6 = (x-2)(x-3) \)

Step 2: Set each factor equal to zero: \( x-2=0 \) or \( x-3=0 \)

Step 3: Solve: \( x=2 \) or \( x=3 \)

Solve \( 2x^2 + 7x + 3 = 0 \) by factoring.

Step 1: Factor: \( 2x^2 + 7x + 3 = (2x+1)(x+3) \)

Step 2: Set each factor to zero: \( 2x+1=0 \) or \( x+3=0 \)

Step 3: Solve: \( x=-\frac{1}{2} \) or \( x=-3 \)

Solve \( x^2 - 7x + 12 = 0 \)
Solve \( x^2 + 2x - 15 = 0 \)
Solve \( 3x^2 - 11x + 6 = 0 \)
Solve \( 4x^2 - 4x - 15 = 0 \)
Solve \( 2x^2 + x - 6 = 0 \)