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 on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degrees of p(x) and g(x)?

If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degrees of p(x) and g(x)?

On dividing the polynomial 2x^(3)+4x^(2)+5x+7 by a polynomial g(x) the quotient and the remainder were 2x and 7-5x respectively.Find g(x)

On dividing the polynomial f(x)=x^3-3x^2+x+2 by a polynomial g(x) , the quotient q(x) and remainder r(x) where q(x)=x-2 and r(x)=-2x+4 respectively. Find the polynomial g(x) .

Find the quotient and remainder when p(x) is divided by q(x)

Answer the following and justify. (i) can x^(2)-1 be the quotient on division of x^(6) +2x^(3) +x - 1 by a polynomial in x of degree 5? (ii) What will be quotient and remainder be on division of ax^(2)+bx +c by px^(3) +qx^(2) +rx +s, p ne 0 ? (iii) If on division of a polynomial p(x) by a polynomial g(x) , the quotient is zero, what is the relation between the degree of p(x) and g(x) ? (iv) If on division of a non-zero polynomial p(x) by a polynomial g(x) , the remainder is zero, what is the relation between the degrees of p(x) and g(x) ? (v) Can be quadratic polynomial x^(2) +kx +k have equal zeroes for some odd integer k gt 1 ?

On dividing the polynomial f(x)=x^(3)-3x^(2)+x+2 by a polynomial g(x), the quotient q(x) and remainder r(x) where q(x)=x-2 and r(x)=-2x+4 respectively.Find the polynomial g(x) .

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in ech of the following p(x) = x^3+4x^2+5x+6,g(x) = x^2+3 .

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : p(x)= x^(4)-5x+6, g(x)= 2-x^(2) .

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : p(x)=x^4-5x+6 , g(x)=2-x^2