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Question
x3 + 2x2 − x − 2
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Solution
Let `f(x) = x^3 + 2x^2 - x-2 ` be the given polynomial.
Now, put the x = -1, we get
\[f( - 1) = \left( - 1 \right)^3 + 2 \left( - 1 \right)^2 - \left( - 1 \right) - 2\]
\[ = 0\]
Therefore, (x +1)is a factor of polynomial f(x).
Now, x3 + 2x2 − x − 2 can be written as,
\[f(x) = x^3 + 3 x^2 - x^2 - 3x + 2x - 2\]
`f(x) = x^2(x -1) + 3x(x-1) + 2(x - 1)`
`= (x-1){x^2 + 3x + 2}`
` = (x - 1)(x + 1) (x+2)`
Hence, (x-1)(x+1)(x+2)are the factors of the polynomial f(x).
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