Question

can (x-3) be the remainder , on the division of polynomial p(x) by (2x+5) ? justify.

Answer 1

(x+3) can not be the reminder on the division of a polynomial p(x) by 2x-5, because the degree of reminder should be less than the degree of divisor. In the given question, the degree of reminder is equal to the degree of divisor. Hence it is not possible.
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Answer 2

It is false

By remainder theorem

on dividing the polynomial P(x) of degree one or more than by a linear polynomial x-a , the remainder obtained is p(a) , where a is a real number .

Here, the divisor 3x+2 and remainder degree is 1 

so x-3 is not the remainder

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