Question

I need an explanation of this pleasee

Answer 1

Option A is wrong because,

only when p(5)=0 , x-5 can be a factor of p(x)
but the question says P(3)=-2

option B is wrong because,

only when p(2)=0 , x-2 can be a factor of p(x)
but the question says P(3)=-2

option C is wrong because,

only when p(-2)=0 , x+2 can be a factor of p(x)
but the question says P(3)=-2

option D is correct because,

only when p(3)=0 , x-3 can be a factor of p(x)
here p(x) is not equal to 0

therefore, p(x)=0+(-2)=-2
so when p(x) is divided by x-3 it will leave a reminder -2

hope it helps!!