Steps for factoring quadratic expressions

Steps for factoring quadratic expressions

1. Find the greatest common factor

   • Find a number that multiplies into all terms, the greatest or largest number is what we are looking for
     • Divide each term in the equation by the gcf you just found in the last steps
       • put the divided terms in the brackets showing you have divided the terms out
         • what you are left with is the greatest common factor

2. difference of squares factoring

   • check if the terms have a greatest common factor and factor it out
     • rewrite the binomial so that each term is written as a squared term, expand the equation
       • subtract between the terms you have just expanded, now simplify
         • before simplifying check to be sure you cant factor anymore
   • identify that the binomial is in fact a difference of squares

3. perfect squares factoring

   • identify that its a perfect squares trinomial, confirm the first and last numbers are perfect squares
     • make sure your middle term is twice the product of your square roots of your first an last terms
       • write the equation to find your gcf
         • expand your equation
           • simplify, rewrite your equation by subtraction and putting like terms together

4. factoring simple trinomials

   • us the sum product rule, find what the first and last numbers multiply to but add up to give middle number or b
     • use these numbers you have found to write out your factors
       • now expand your factors
         • simplify

5. Factoring complex trinomials

   • Multiply the x squared and plain coefficent together
     • list the numbers of the steps above
       • find which factors in the list add to give the x middle coefficent
         • rewrite the quadratic into 4 like terms
           • split the quadratic into 2 and factorise to give 2 identical brackets
             • rewrite into 2 brackets
     • make sure no common factor exists