The polynomial `p(x)` is such that for any polynomial `q(x)` we have `p(q(x))=q(p(x))` then `p(x)` is

On dividing a polynomial p(x) by a non-zero polynomial q(x) , let g(x) be the quotient and r(x) be the remainder then = q(x)* g(x) + r(x), where

If x^(p^(q))=(x^(p))^(q), then p=

If the polynomial P(x)=2x+x-5x^(2)-x+1 is divided bythe polynomial Q(x)=x^(2)-x then the remainder is alinear polynomial R(x)=ax+b. Then (a+b) equals:

Let P and Q be polynomials. Find Lim_(x->oo) (P(x))/(Q(x)) if the degree of P is

Find a zero of the polynomial (i) p(x)=x-3 (ii) q(x)=3x+2

If 2 and -2 are the zeroes of the polynomial p(x). write the polynomial p(x)

If we divide a polynomial p(x) by x-alpha, the remainder obtained is p(alpha) Note that if p(alpha)=0, then x-alpha is a factor of p(x)

Let p_1(x) = x^3 – 2020x^2 + b_1x + c_1 and p_2(x) = x^3 – 2021x^2 + b_2x + c^2 be polynomials having two common roots alpha and beta . Suppose there exist polynomials q_1(x) and q_2(x) such that p_1(x)q_1(x) + p_2(x)q_2(x) = x^2 – 3x + 2 . Then the correct identity is

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)?