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Question
x3 − 6x2 + 3x + 10
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Solution 1
Let f(x) = x3 − 6x2 + 3x + 10 be the given polynomial.
Now, putting x = -1we get
`f(-1) = (-1)^3 - 6(1)^2 + 3(-1) + 10`
` = -1 -6 -3 + 10`
` = -10 + 10`
` = 0`
Therefore, (x+1)is a factor of polynomial f(x).
Now,
\[f(x) = x^3 - 7 x^2 + x^2 + 10x - 7x + 10\]
`f(x) = x^2 (x + 1) - 7x(x+1)+10(x +1)`
` =(x +1){x^2 - 7x + 10} `
` = (x+1){x^2 - 5x - 2x + 10}`
` = (x+1)(x-5)(x-2)`
Hence, (x+1),(x-2) and (x-5) are the factors of the polynomial f(x).
Solution 2
Let f(x) = x3 − 6x2 + 3x + 10 be the given polynomial.
Now, putting x = -1we get
`f(-1) = (-1)^3 - 6(1)^2 + 3(-1) + 10`
` = -1 -6 -3 + 10`
` = -10 + 10`
` = 0`
Therefore, (x+1)is a factor of polynomial f(x).
Now,
\[f(x) = x^3 - 7 x^2 + x^2 + 10x - 7x + 10\]
`f(x) = x^2 (x + 1) - 7x(x+1)+10(x +1)`
` =(x +1){x^2 - 7x + 10} `
` = (x+1){x^2 - 5x - 2x + 10}`
` = (x+1)(x-5)(x-2)`
Hence,(x+1),(x-2) and (x-5) are the factors of the polynomial f(x).
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