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Question
y3 − 7y + 6
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Solution
Let f(y) =y3 − 7y + 6 be the given polynomial.
Now, putting y= 1,we get
`f(y) = (1)^3 -7(1) + 6 = 1-7 +6`
` = 7-7 = 0`
Therefore, (y-1)is a factor of polynomial f(y).
Now,
`f(y) = y^2 (y-1) + y(y-1) -6(y-1)`
` = (y-1){y^2 + y y-6}`
` = y-1{y^2 + 3y - 2y - 6}`
`= (y -1)(y+2)(y+3)`
Hence (y-1),(y-2) and (y+3)are the factors of polynomial f (y).
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