Steps for fatoring quadratic expressions

Steps for fatoring quadratic expressions

1. Look for a greatest common factor (GCF)

   • Yes, there is a GCF (6a^2-15a = 3a(2a-5) 3a=GCF)
     • Factor out GCF. Can you factor again?
       • Yes
         • Continue and look which route to take to factor further
       • No.
   • No, there is not a GCF
     • Is the expression a difference of squares? Must be binomial, both terms are a perfect square and there must be a subtraction.
       • Yes. Factor using the square roots of each term. x^2-36 = (x-6)(x+6)
       • No.
         • Is the expression a perfect square trinomial? Two identical binomials.
           • Yes. Factor using the square root of the first and last term. The middle term must be double the product of the roots of the other terms. 4x^2-24x+36 = (2x-6)(2x-6) = (2x-6)^2 . Square roots of terms are 2 and 6.
           • No.
             • Is the expression a simple trinomial ( y=ax^2+bx+c a=1)
               • Yes. Use Sum and Product method (trial and error).
                 • x^2+13x+12 = (x+1)(x+12)
               • No.
                 • Is it a complex trinomial ( y=ax^2+bx+c a = +1)
                   • Yes. Factor using decomposition method. Find two numbers that add to 'b' and multiply to 'ac'
                     • 6x^2-13x-5 = 6x^2-15x+2x-5 = 3x(2x-5)+1(2x-5) = (3x+1)(2x-5)