Steps for Factoring Quadratic equations

Steps for Factoring Quadratic equations

1. 1 factoring out the greatest common factor

   • 2 differences of squares factoring
     • 3 perfect square trinomial factoring
       • 4 factoring simple trinomials
         • 5 factoring complex trinomials
           • factoring complex trinomials is different that factoring simple trinomials because the coefficient of the squared x is not always one so for example 6x²-13x-5 we first find two numbers that add to -13 and multiply to 6*-5 (-30) we need to use the product of the first and the last number which is -30. So two numbers that add to -13 and multiply to -30 are -15 and 2. the middle term can now be written as -15+2 which is equal to -13. Now we have 6x²-15x+2x-5 now we can factor out the GCF out of both sets of terms wich is
         • a simple trinomial is an expressoin x²+13x+12 then to factor it you need to find two numbers that add to get the middle number and multiply to get the last number 12 and 1 are the numbers so the answer is (x+12) (x+1) this is called the sum and product methodd
       • perfect squares factoring is if you have a expression (2x-4)(2x-4) and you need to factor so you use foil and expand and then you get 4x²-8x-8x=16 simplify and you get 4x²-16x+16 and this is your factored form
     • Differences of squares is when you have (x+6) (x-6) and you need to factor. So you use foil and expand and then you have x²+6x-6x-36 then you simplify and you get x² -36 as your factored form
   • GCF is the greatest numerical factor that divides into all the terms.
     • After you have the gcf then you divide all the terms by the gcf example factor 6x-3 the greatest common factor is 3 so 6x/3-3/3=3(2x-0)