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Step-by-step explanation:
Start with Trial and Error.
Take x - 1
x - 1 = 0
x = 1
p(x) = x^3 - 2x^2 - x + 2
p(2) = (1)^3 - 2(1)^2 - (1) + 2
= 1 - 2 - 1 + 2
= 0
Since the remainder is zero, you can do long division.
The quotient will be x^2 - x - 2.
Then split the middle term of the quotient.
x^2 - x - 2
= x^2 - x + 2x - 2
Then take the common factor out.
x^2 - x + 2x - 2
= x(x - 1) + 2(x - 1)
Then take (x - 1) out as it is common.
x(x - 1) + 2(x - 1)
= (x - 1)(x + 2)
(x - 1)(x + 2) is your answer.
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