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
ex. 3x2-8x-16=0 p= -48
s= -8 -12 and +4 are the factors
(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(w+4)=60 or w2+4w=60
w=-10 or 6 has to be the positive answer, so width=6ft and length=10 ft