Question

2y³ − 5y² − 19y + 42

Answer 1

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).