Solve a quadratic equation by factoring

A quadratic equation is an equation that can be written as

ax ² + bx + c where a ≠ 0

A quadratic equation must have a squared term as its highest power

Examples of quadratic equations
• y = 2x² + 3x + 7
• y = 13x² + 2
• y = x² − 4x + 15
• y = −x² + 5

Examples of equations that are not quadratic
• y = 11x + 223
• y = x³ − 4x² +5x +6
• y = 2x³ − 7x²
• y = −x⁴ + 5

The solution of a quadratic equation is the value of x when you set the equation equal to zero
i.e. When you solve the following general equation: 0 = ax² + bx + c

Given a quadratic equation: ax ² + bx + c

One method to solve the equation for zero is to factor the equations.
General Steps to solve by factoring
• Step 1) Create a factor chart for all factor pairs of c
  • A factor pair is just two numbers that multiply and give you 'c'
• Step 2) Out of all of the factor pairs from step 1, look for the pair (if it exists) that add up to b
  • Note: if the pair does not exist, you must either complete the square or use the quadratic formula .
• Step 3) Insert the pair you found in step 2 into two binomals
• Step 4) S olve each binomial for zero to get the solutions of the quadratic equation.