1.a polynomial f(x) leaves remainder 15 and (2x+1) when divided by (x-3) and (x-1)^2 respectively.then,what is the remainder when it is divided by (x-3){(x-1)^2}

2.find all polynomials P satisfying p(x+1)=p(x)+2x+1

3.if all the roots of the polynomial equation

x^4-4x^3+ax^2+bx+1=0 are positive real numbers,show that all the roots are equal.

please help!

question 2:

i have observed that p(x)=x^2 satisfies the given condition.do we now have to substitute p(x) in the condition ?

how should we substitute?