Steps to factoring Quadratic Expressions

Steps to factoring Quadratic Expressions

1. Determine method of factoring

   • Factoring out GCF
     • Step One: determine GCF
       • Step Two: divide all terms by GCF
   • Difference of Squares
     • Step One: determine if expression is difference of squares
       • Step Two: factor using the square roots of each term
   • Perfect Square Trinomials
     • Step One: determine if the expression is a perfect squares expression
       • Step Two: factor using the squares roots of each term
   • Factoring Simple Trinomials
     • Step One: factor out GCF (if necessary) and determine method of factoring.
       • Step Two: determine two numbers that have a product of 'c' and a sum of 'b'.
         • Step Three: write the numbers in binomials with appropriate variables and corresponding operations.
   • Factoring Complex Trinomials
     • Step One: find two numbers with a sum of 'b' and a product of 'a⋅c'
       • Step Two: "decompose" the middle term
         • Step Three: factor out GCF for first and last two terms
           • Step Four: factor out binomials in brackets.

2. To be a Perfect Squares expression, two things must be true: one, the first and last terms must be perfect squares. Two, the middle term must double the product of the roots of the other two terms.

3. The GCF has two parts.: the greatest common numerical factor that can divide equally into all terms, and the greatest variable factor that can divide evenly into all terms

4. To be a Difference of Squares expression, three things must be true: one, the expression must be a binomial. Two, both terms must be a perfect square. Three, There must be a subtraction between the terms.

5. A simple trinomial is in the form of y = ax² + bx + c, with a = 1

6. A complex trinomial is in the form of y = ax² + b + c, with a ≠ 1