Question

factorise 2y³+y²-2y-1

Answer 1

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)