Given: 5y^2 + 43y - 185y2+43y−18
Using the AC-method from Ay^2 + By + C = 0Ay2+By+C=0:
A*C = 5 (-18) = -90A⋅C=5(−18)=−90
We need to find two numbers, mm, and nn such that they multiply to -90−90 and add to 4343. Since 4343 is positive, the largest number must be positive. This is the number that will be multiplied with 5y5y 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)
