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Question
2y3 − 5y2 − 19y + 42
Solution
Let f(y) =2y3 − 5y2 − 19y + 42 be the given polynomial.
Now, putting y=2,we get
`f(2) = 2(2)^3 - 5(2)^2 - 19(2) + 42`
` = 16 - 20 - 38 + 42 = -58 + 58`
` = 0`
Therefore, (y - 2)is a factor of polynomial f(y).
Now,
`f(y) = 2y^2 (y-2) - y(y - 2) -21(y - 2)`
` = (y -2){2y^2 - y - 21}`
` = (y-2){2y^2 - 7y + 6y - 21}`
` = (y-2)(y + 3)(2y - 7)`
Hence (y - 2),(y+3) and (2y - 7) are the factors of polynomial f(y).
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