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Question
x3 − 3x2 − 9x − 5
Solution
Let `f(x) = x^3 - 3x^2 - 9x -5 ` be the given polynomial.
Now, putting x = 1,we get
`f(-1) = (-1)^3 -3(-1)^ -9(-1) - 5`
`=-1 -3 +9 -5 = -9 +9 = 0`
Therefore, (x + 1)is a factor of polynomial f(x).
Now,
`f(x) = x^2 (x+1) -4x(x+1) -5(x +1)`
` = (x+1){x^2 -4x -5}`
` =(x+1){x^2 - 5x + x -5}`
` = (x+1)(x+1)( x-5)`
Hence (x+1) , (x+1) and (x - 5) are the factors of polynomial f(x) .
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