Question

Find the number that must be subtracted from the polynomial 3y³ + y² – 22y + 15, so that the resulting polynomial is completely divisible by y + 3. 

Answer 1

let the number to be subtravted from the given polyomial be k 

let f(y) =3y^3+y^2-22y15-k 

it is given that f(y)  is divisible by (y+3) 

remainder=f(-3)=0 

3(-3)^3+(-3)^2-22(-3)+15-k=0 

-81+9+66+15-k=0 

9-k=0 

k=9