Given: f(x) = 2x3 – 7x2 – 3x + 18
By hit and trial method
For x = 2, the value of f(x) will be
f(2) = 2(2)3 – 7(2)2 – 3(2) + 18
= 16 – 28 – 6 + 18 = 0
As f(2) = 0, (x – 2) is a factor of f(x).
Now, performing long division we have
Therefore, factorized form of f(x) is,
f(x) = (x – 2) (2x2 – 3x – 9)
= (x – 2) (2x2 – 6x + 3x – 9)
= (x – 2) [2x(x – 3) + 3(x – 3)]
= (x – 2) (x – 3) (2x + 3)
Now, for f(x) = 0 we get roots as,
(x – 2) (x – 3) (2x + 3) = 0
Hence x = 2, 3 or -3/2