Determine what must be added to x3-3x2+4x-13. . .

Question : Determine what must be added to (x³-3x²+4x-13) to obtain a polynomial which is exactly divisible by x-3.

Doubt by Bhavya

Solution : 

Let
p(x)=x³-3x²+4x-13
g(x)=x-3

Now, let's find out what should be the remainder when p(x) is divided by g(x)

By Remainder Theorem

g(x)=0
x-3=0
x=3

p(3)=(3)³-3(3)²+4(3)-13
p(3)=27-27+12-13
p(3)=0-1
p(3)=-1

Hence -p(3) i.e. -(-1)=1 should be added to the polynomial so that it p(x) would be completely divisible by x-3.