Steps for Factoring QuadraticExpressions

Steps for Factoring QuadraticExpressions

1. is There a GCF

   • No
     • What type of expression.
       • Simple Ex. x^2 + 6x - 16
         • use sum and product method: determine two numbers that multiply to (c) and add to (b) and finally write the numbers from the previous step in binomials with the appropriate variables
       • Complex Ex. 3x^2 - 7x - 6
         • decomposition method
           • determine two numbers that multiply to ‘a∙c’ and add to ‘b’ and then decompose the middle term from the previous step, factor out the greatest common factor of the first two terms and the last two terms finally factor out the common binomial factor.
         • trial and error method
           • Find two factors of variable a and find two factors of variable c then cross multiply the variables so as to add to variable b
       • Perfect square trinomial Ex. 4x^2 - 24x + 36 = (2x - 6)^2
         • how to solve: factor using the square roots of each term
       • Difference of squares Ex. x^2 - 36 = (x - 6)(x + 6)
         • how to solve: factor using square roots of each term
   • yes
     • Factor out the GCF