Find all polynomials p satisfying `p(x+1)=p(x)+2x+1.`

Let p(x) be a polynomial function satisfying p(x)+p(2x)=5x^(2)-18 then the value of sum_(x=1)^(5)p(x)=

The number of polynomials p:R to R satisfying p(0)=0,p(x) gtx^(2) for all x ne0 , and p''(0)=(1)/(2) is

The number of cubic polynomials p(x) satisfying p(1)=2, p(2)=4, p(3)=6, p(4)=8 is

Find all cubic polnomials p(x) such that (x-1)^(2) is a factor of p(x)+2 and (x+1)^(2) is a factor of p(x)-2 .

If P(x) is a polynomial of degree 3 satisfying p(-1)=10,p(1)=-6 and p(x) has maxima at x=-1 and p'(x) has minima at x=1, find the distance between the local maxima and local minima of the curve.

If p(x) is a polynomial of degree 3 satisfying p(-1)=10 , p(1) =-6 and p(x) has maxima at x=-1 and p'(x) has minima at x=1, find the distance between the local maxima and local minima of the curve.

If p(x) is a polynomial of degree 3 satisfying p(-1)=10 , p(1) =-6 and p(x) has maxima at x=-1 and p'(x) has minima at x=1, find the distance between the local maxima and local minima of the curve.

If p(x) be a polynomial satisfying the identity p(x^2)+2x^2+10x=2xp(x+1)+3 , then p(x) is given by

P(x) be a polynomial of degree 3 satisfying P(-1) =10 , P(1) =-6 and p(x) has maxima at x = -1 and p(x) has minima at x=1 then The value of P(2) is