steps for factoring Quadratic Expressions

steps for factoring Quadratic Expressions

1. Decomposition

   • (ax^2+bx+c)a does not = 1
     • find GCF
       • find two numbers that add to 'b' and multiply to c
         • break down middle term
           • factor out GCF
             • factor out binomial in brackets
               • ex) (6x^2 - 13x -5) 6x-5 = -30, -15 x2= -30, -15+2= -13
                 • =6x^2 -15x +2x -5
                   • =3x(2x-5) 1(2x-5)
                     • =(3x-1) (2x-5)

2. Trail and error

   • (ax^2 + bx + c) a does not = 1
     • find two factors of the first and last term and list them below
       • multiply factors diagonally
         • add together the results
           • sum should equal coeffient of middle term
             • first row creates 1st binomial and second row creates 2nd binomial
               • ex)

3. sum and product

   • (ax^2 + bx + c) a = 1
     • find GCF
       • find 2 terms that add to b and multiply to c
         • ex) x^2 - 9
           • = x^2 + 0x -9
             • -3x + 3 = 0 / -3x x 3 = 9
               • = (x + 3) (x - 3)

4. perfect square trinimal

   • ax^2 + bx + c
     • square root a and c
       • ex) 4x^2 - 12x + 9
         • =(2x-3) (2x-3)
           • = (2x - 3)^2

5. square of difference

   • includes; 2 terms and both are perfect squares
     • find GCF
       • square root both terms
         • ex) x^2 - 9
           • = x-3
             • = (x-3) (x-3)