Let `p(x)=(x-1)(x-2)(x-3)` for how many polynomials `R(x)` of degree 3 such that `P(Q(x))=P(x).R(x)` ?

Assertion : 3x^(2)+x-1=(x+1)(3x-2)+1 . Reason : If p(x) and g(x) are two polynomials such that degree of p(x)ge degree of g(x) and g(x)ge0 then we can find polynomials q(x) and r(x) such that p(x)=g(x).q(x)+r(x) , where r(x)=0 or degree of r(x)lt degree of g(x) .

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

If (x-3) and (x-1/3) are factors of the polynomial px^(2)+3x+r , show that p=r.

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) 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.

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 2 and P(3)=0,P'(0)=1,P''(2)=2," then "p(x)=

Assertion (A): p(x)=14x^(3)-2x^(2)+8x^(4)+7x-3 is a polynomial of degree 3. Reason (R):The highest power of x in the polynomial p(x) is the degree of the polynomial.