Given: #5y^2 + 43y - 18#
Using the AC-method from #Ay^2 + By + C = 0#:
#A*C = 5 (-18) = -90#
We need to find two numbers, #m#, and #n# such that they multiply to #-90# and add to #43#. Since #43# is positive, the largest number must be positive. This is the number that will be multiplied with #5y# when you distribute using FOIL.
#ul(" "m" "|" "n" "| " "m*n = -90" "|" "m+n = 43" ")#
# " "-1" "|" "90" "|"" -1*90 = -90" "| -1 + 90 != 43#
# " "-2" "|" "45" "|""-2*45 = -90" "| -2 + 45 = 43#
Break the middle term #43y# into #ny + my#:
#5y^2 + 43y - 18 = 5y^2 + 45y -2y - 18#
Factor by group factoring:
#(5y^2 + 45y) + (-2y - 18) = 5y(y+9) - 2(y+9)#
#(5y - 2)(y+9)#
#5y^2 + 43y - 18 = (5y - 2)(y+9)#
