• Product Sum III
     
     This version of the product-sum we use in trinomials (ax2+bx+c) when the a value is more than 1.  Remember the two factors are used to split the middle term into two terms then we factor in pairs.

    ex. 6x2+19x+15   p= 6*15= 90
                              s= 19     9 and 10 would be the two factors

         6x2+10x+9x+15    we split the middle term, now factor by pairs

         6x2+10x+9x+15
         2x(3x+5)+3(3x+5)
         (3x+5)(2x+3)

    ex.  3x2-8x-16=0   p= -48
                                s= -8    -12 and +4 are the factors

          3x2-12x+4x-16=0
          3x(x-4)+4(x-4)=0
          (x-4)(3x+4)=0       now use zero product property to solve

          x= 4 or -4/3

    ex. In a rectangular garden, the length is 4 more than the width.  If the area of the garden is 60 ft2 what are the dimensions?

     w=width
     w+4=length

     w(w+4)=60 or w2+4w=60
    so w2+4w-60=0
    (w+10)(w-6)=0
    w=-10 or 6  has to be the positive answer, so width=6ft and length=10 ft