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