Using factor theorem, factorize each of the following polynomial:
2y3+y2-2y-1
Let, f (y) = 2y3+y2-2y-1
The factors of the constant term - 1 are
The factor of the coefficient of y3 is 2. Hence, possible rational roots are
We have
f (1) = 2 (1)3 + (1)2 – 2 (1) - 1
= 2 + 1 – 2 - 1
= 0
So, (y - 1) is a factor of f (y)
Let us now divide
f (y) = 2y3+y2-2y-1 by (y - 1) to get the other factors of f (x)
Using long division method, we get
2y3+y2-2y-1 = (y - 1) (2y2 + 3y + 1)
2y2 + 3y + 1 = 2y2 + 2y + y + 1
= 2y (y + 1) + 1 (y + 1)
= (2y + 1) (y + 1)
Hence, 2y3+y2-2y-1 = (y - 1) (2y + 1) (y + 1)