Relation Between Dividend, Divisor, Quotient and Remainder

When polynomial $f\left(x\right)=x^4 +2x^3 -3x^2 +x-1$ is divided by $(x - 2)$, then what will be remainder?

On dividing $x^3-3x^2+5x-7$ by $x^2-2x+4$, if the remainder is in the form of $Ax+B$ then find the values of $A\text{ and} B$.

How are we supposed to divide a polynomial by a monomial?

Find roots of the cubic polynomial $x^3+8x^2+17x+10=0$.

Divide the polynomial $P\left(x\right)=x^3-3x^2+5x-3$ by the polynomial $g\left(x\right)=x^2-2$ and find quotient and remainder.

${(x^2+2x+1)}^2÷x^2$

Let $f\left(x\right)$ be a polynomial function. If $f\left(x\right)$ is divided by $x-1, x+1 \& x+2,$ then remainders are $5, 3$ and $2$ respectively . When $f\left(x\right)$ is divided by $x^3+2x^2-x-2,$ then remainder is :

Divide $5x^2-25x+20$ by $x-4$.

Divide $4x^3+4x^2-x+1$ by $x+1$.

$C_0{C}_r+C_1{C}_{r+1}+C_2{C}_{r+2}+\dots +C_{n-r}{C}_n$ is equal to

Using division algorithm, find the divisor of $\left(x^2+3x-12\right)$, which gives quotient as $\left(x-3\right)$ and remainder $6$. 

Find the remainder when: $x^3+x^2-11x+12$ is divided by $x+4$ and also mention the dividend.

Find the remainder when: $x^4+2x^3-5x^2-2x+8$ is divided by $x+1$. Also, mention the divisor.

If one factor of the polynomial $x^3+4x^2-3x-18$ is $x+3$, then the quotient is ___

On dividing $3x^3+x^2+2x+5$ by a polynomial $g\left(x\right)$, the quotient and remainder are $(3x-5)$ and $(9x+10)$ respectively. Find $g\left(x\right)$

On dividing $3x^3 – 8x + 5$ by $x – 1$, the remainder is

If $3x^2-x^3+5x-2$ is divided by $x-1+x^2$, then the remainder is

Polynomial $x^4+x^3-2x^2+x+1$ is divided by $x-1$, the remainder will be

What is meant by a divisor in the division of polynomials? 

When $p\left(x\right)\text{ and }q\left(x\right)$ are divided by $x^2+2x+3$ then the remainders are $x+2\text{ and }x+4$ respectively. What is the remainder when $p\left(x\right)·q\left(x\right)$ is divided by $x^2+2x+3$?