Let `P(x)=P(0)+P(1)x+P(2)x^(2)` be a polynomial such that `P(-1)=1` ,then `P(3)` is :

Let P(x)=x^(4)+ax^(3)+bx^(2)+cx+d be a polynomial such that P(1)=1,P(2)=8,P(3)=27,P(4)=64 then find P(10)

Let P(x)=x^(4)+ax^(3)+bx^(2)+cx+d be a polynomial such that P(1)=1,P(2)=8,+P(3)=27,P(4)=64 then the value of 152-P(5) is

If P(x) is a polynomial such that P(x^(2)+1)={P(x)}^(2)+1 and P(0)=0, then P'(0) is equal to

Let P(x) and Q(x) be two quadratic polynomials such that minimum value of P(x) is equal to twice of maximum value of Q(x) and Q(x)>0AA x in(1,3) and Q(x)<0AA x in(-oo ,1)uu(3, oo) If sum of the roots of the equation P(x) =0 is 8 and P(3)-P(4)=1 and distance between the vertex of y=P(x) and vertex of y=Q(x) is 2sqrt(2) The polynomial P(x) is:

Let P(x) and Q(x) be two quadratic polynomials such that minimum value of P(x) is equal to twice of maximum value of Q(x) and Q(x)>0AA x in(1, 3) and Q (x)<0AA x in(-oo, 1)uu(3, oo) . If sum of the roots of the equation P(x)=0 is 8 and P(3)-P(4)=1 and distance between the vertex of y=P(x) and vertex of y=Q(x) is 2sqrt(2) The polynomial P(x) is:

Let P(x) be a polynomial such that P(1)=1 and (p(2x))/(p(x+1))=8-(56)/(x+7) for all real x for which both sides are defined.The degree of P(x) is

P(x) is said to be a monic polynomial if its leading coefficient is 1. If P(x) is divided b (x-a) the remainder is given by P(a). If P(a) = 0 then (x-a) is called factor of P(x). If P(x) is a monic polynomial of degree 4 such that P(1) = P(2) = P(3) = P(4) = 2. The value of P(0) is

Let P be a non-zero polynomial such that P(1+x)=P(1-x) for all real x, and P(1)=0. Let m be the largest integer such that (x-1)^m divides P(x) for all such P(x). Then m equals