Let p(x) = x3 − 2x2 − x + 2
All the factors of 2 have to be considered. These are ± 1, ± 2.
By trial method,
p(2) = (2)3 − 2(2)2 − 2 + 2
= 8 − 8 − 2 + 2 = 0
Therefore, (x − 2) is factor of polynomial p(x).
Let us find the quotient on dividing x3 − 2x2 − x + 2 by x − 2.
By long division,
It is known that,
Dividend = Divisor × Quotient + Remainder
∴ x3 − 2x2 − x + 2 = (x + 1) (x2 − 3x + 2) + 0 = (x + 1) [x2 − 2x − x + 2]
= (x + 1) [x (x − 2) − 1 (x − 2)] = (x + 1) (x − 1) (x − 2)
= (x − 2) (x − 1) (x + 1)