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?