Question

factorise 2y3+y2-2y-1

Answer 1

Sol:
Let f(y) = 2y3 + y2 - 2y - 1.
Substitute y = 1 then f(y) = 0
y -1 is a factor of 2y3 + y2 - 2y - 1.

         y - 1 ) 2y3 + y2 - 2y - 1 ( 2y2 +3y +1
                  2y3 - 2y2   (substract)
                -----------------------------
                        3y2 - 2y - 1
                        3y2 -  3y  (substract)
                      ---------------------------------------
                                y -1
                                y -1  (substract)
                               ---------------
                                  0
∴ The quotient is 2y2 +3y +1 = 0
                  2y2 +2y + y +1 + 0
                  2y(y + 1) +1(y +1) =0
                 2y + 1 = 0 ,y + 1 = 0
y = -1/2 , -1 .

∴ 2y3 + y2 - 2y - 1 = ( y - 1)( 2y + 1)(y +1).