Tag: division algorithm for polynomials

$p(x)=(x^2-10x-24)$ , 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 $p$.

The remainder obtained when the polynomial $1+x+x^ {3}+x^ {9}+x^ {27}+x^ {81}+x^ {243}$ is divisible by $x-1$ is

If $A=2x^{3}+5x^{2}+4x+1$ and $B=2x^{2}+3x+1$, then find the quotient from the following four option, when A is divided by B.

Evaluate: $\displaystyle \frac{a^3\, +\, b^3\, +\, c^3\, -\, 3abc}{a^2\, +\, b^2\, +\, c^2\, -\, ab\, -\, bc\, -\, ca}$

If x + 2 and x-1 are the factors of $x^3 + 10x^2+mx + n$, then the values of m and n are respectively