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प्रश्न
x3 − 10x2 − 53x − 42
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उत्तर
Let `f(x) = x^3 - 10x^2 - 53x -42` be the given polynomial.
Now, putting x = -1 we get
`f(-1) = (-1)^3 - 10(-1)^2 - 53(-1) - 42`
` = -1-10 + 53 - 42`
` = -53 + 53 = 0`
Therefore, (x + 1)is a factor of polynomial f(x).
Now,
`f(x) = x^2 (x+1) -11x(x+1) - 42(x+1)`
` = (x+1){x^2 -11x - 42}`
` = (x + 1){x^2 - 14x + 3x - 42}`
` = (x +1)(x+3)(x - 14)`
Hence (x+1),(x + 3) and (x - 14)are the factors of polynomial f(x).
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