Tag: remainder and factor theorems

$p(x)=(x^2-10x-24)$ , when divided by $x+2$ and $x\neq -2$ gives the quotient $Q$. Find $Q$.

When $(x^3-2x^2+px-q)$ is divided by $(x^2-2x-3)$, the remainder is $(x-6)$. The values of $p$ and $q$ respectively are ____. 

When a polynomial $P(x)$ is divided by $x, (x - 2)$ and $(x - 3)$, remainders are $1$, $3$ and $2$ respectively. the same polynomial is divided by $x(x - 2)(x - 3)$, the remainder is $ax^2 + bx + c$, then the value of $c$ is

The quotient and remainder when $x^{2002}$ $- 2001$ is divided by $x^{91}$ are 

Which of the following given options is/ are correct?
If $p(x)=q(x)g(x)+r(x)$ (By Division Algorithm) where p(x), g(x) are any two polynomials with $g(x)\neq 0$, then

A polynomial $f(x)$ with rational coefficient leaves reminder $15$, when divided by $(x-3)$ and remainder $2x+1$, when divided by $(x-1)^{2}$. If $p$ is coefficient of $x$ of its remainder which will come out if $f(x)$ is divided by $(x-3)(x-1)^{2}$ then find $p$.