Given the following function:
[tex]\text{ 3y}^2\text{ - 2y - 5 = (y + 1)(?)}[/tex]Let's determine the missing factor:
[tex]\text{ 3y}^2\text{ - 2y - 5 = (y + 1)(?)}[/tex][tex]\text{ 3y}^2\text{ - 2y - 5 = (y + 1)(A + B)}[/tex]Where:
[tex]\text{ A = }\frac{3y^2}{y}\text{ = 3y}[/tex][tex]\text{ -2y = By + }(1)A[/tex][tex]\text{ -2y = By + }(1)\text{(3y)}[/tex][tex]\text{ -2y = By + 3y}[/tex][tex]\text{ -2y - 3y = By}[/tex][tex]\text{ -5y = By}[/tex][tex]\text{ }\frac{\text{-5y}}{\text{ y}}\text{ = }\frac{\text{By}}{\text{ y}}[/tex][tex]\text{ -5 = B}[/tex]Therefore, the missing factor will be:
(y + 1)(A + B) = (y + 1)(3y - 5)
The answer is 3y - 5
