What should be added to the polynomial  $x^3-3x^2+6x-15$ so that it is completely divisible by 𝑥 − 3.

We are given a polynomial . Firstly, we will find its remainder when divided by 𝑥 − 3.

We can represent in the form of 𝑏𝑞 + 𝑟 ,

where, 𝑏 is the divisor, 𝑞 is the quotient and 𝑟 is the remainder.

 = 𝑏𝑞 + 𝑟, Where 𝑏 = 𝑥 − 3

$\Rightarrow x^3-3x^2+6x-15=(x-3)\left(x^2+6\right)+3$

ℎ𝑒𝑟𝑒 𝑟 = 3 

⇒Remainder = 3 

Hence, if this remainder is subtracted from the polynomial, it becomes completely divisible by 𝑥 − 3.

Hence, − 3 must be added to the polynomial.