Ineed an explanation of this
for a polynomial p x( ), the value of p(3) is −2. which of the following must be true about p x( ) ?
a) x − 5 is a factor of p x( ).
b) x − 2 is a factor of p x( ).
c) x + 2 is a factor of p x( ).
d) the remainder when p x( ) is divided by x − 3 is −2

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!!