• Product Sum Method 


     

    The Product Sum method of factoring we use on trinomials (ax2+bx+c) with the value of a=1.  This is the method that is probably used the most.
    example:    x2+7x+12 The product is the a value times the c value.  In this case 12.
    The sum is the b value.  In this case 7.
    Find the two numbers that multiply to 12 (the product) andadd to 7 (the sum).        +4 and +3
    These are your two factors.  In your two binomials put the x in front and the factors in the back.   (x+4)(x+3)
    This is your factored expression.  To check FOIL back out.
    Why does this work???
    example:  
    x2-4x-12
     
    p= -12
    s= -4     factors are -6 and +2
    so factored answer is (x-6)(x+2)
    example:
     I'm thinking of a number that could be solved by  x2+10x+16=0.  What could the number be?
    p=16
    s=10    factors are +8 and +2
    (x+8)(x+2)=0
    so either x+8=0 or x+2=0  so either x= -8 or -2 is the 
    number.

     
    For extra help go to
          http://www.algebra-online.com/