Question

y³ − 7y + 6

Answer 1

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).