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Question
x3 − 2x2 − x + 2
Solution
Let `f(x) = x^3 - 2x^2 - x + 2` be the given polynomial.
Now, putting x =1,we get
`f(1) = (1)^3 - 2(1)^2 - (1) + 2`
` = 1-2 - 1+2 = 3 -3`
` = 0`
Therefore, (x+1)is a factor of polynomial f(x).
Now,
`f(x) = x^2 (x-1) -x(x -1) -2(x -1)`
` = (x -1){x^2 - x - 2}`
` = (x -1){x^2 - 2x + x -2}`
` = (x - 1)(x+1)(x - 2)`
Hence (x -1),(x+1) and (x -2)are the factors of polynomial f(x).
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