Factorise
2y3 + y2 - 2y - 1
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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).
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).
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