Question

Find the number that must be subtracted from the polynomial $3^3+y^2-22y+15,$ so, that the resulting polynomial is completely divisible by y + 3.

Answer 1

Let the number to be subtracted from the given polynomial be k.
Let f(y) = 3$y^3$ + $y^2$ – 22y + 15 – 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