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 subtracted from the given polynomial be k.

Let f(y) = 3y³ + y² – 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