Let `P(x)=x^4+a x^3+b x^2+c x+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)=x^(3)-1 then the value of P(1)+P(-1) 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(5) 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

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) be a polynomial of degree 11 such that P(x) = (1)/(x + 1) for x = 0, 1, 2, 3,"…."11 . The value of P(12) is.

If P (x) is polynomial of degree 4 such than P (-1)=P (1) =5 and P (-2) =P(0)=P (2) =2 find the maximum vaue of P (x).

If P(x) is a polynomial such that P(x)+P(2x)=5x^2-18 , then lim_(xrarr3) (P(x))/(x-3) , is

Let f(x)= x^(3) + x + 1 and P(x) be a cubic polynomial such that P(0) = -1 and roots of f(0) = 1 ; P(x) = 0 are the squares of the roots of f(x) = 0 . Then find the value of P(4).

Let P(x) = x^10+ a_2x^8 + a_3 x^6+ a_4 x^4 + a_5x^2 be a polynomial with real coefficients. If P(1)=1 and P(2)=-5 , then the minimum-number of distinct real zeroes of P(x) is

Let X and Y be two events such that P(X)=1/3, P(X|Y)=1/2and P(Y|X)=2/5. Then