Question

Factorise 2y³+y²-2y-1 by using factor theorem

Answer 1

P =  2 y³  + y² - 2 y - 1
multiply coefficients of  y^3 and constant term :  2 *1 =2.
factors of 2 =  +2, -2, 1 , -1    with positive and negative signs.   these four values are possible roots of the given polynomial.

trying them we get  -1, +1 as roots,  as  P(-1) and P(1) = 0
   
      P = (y+1) (y-1) (ay +b)   

now comparing coefficients of y^3 we get a =2,,   
comparing constant term ,  b = 1... check other coefficients too...

P = (y +1 ) ( y - 1) ( 2 y +1 )