Division Algorithm for Polynomials

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

State division algorithm for polynomials.

If $2$ and $-2$ are two zeros of the polynomial $2x^4-5x^3-11x^2+20x+12$, find all the zeros of the given polynomial.

Obtain other zeroes of the polynomial $f\left(x\right)=2x^4+3x^3-5x^2-9x-3$, if two of its zeroes are $\sqrt{3}$ and $-\sqrt{3}$.

What is the quotient and remainder of $\left(2x^3-8x^2+16x-30\right)÷\left(2x^2+x-1\right)$.

What is the quotient and remainder of $\left(4x^3+5x^2-2x+8\right)÷\left(2x+1\right)$.

A polynomial $f\left(x\right)$ with rational coefficients leaves remainder $15$, when divided by $x-3$ and remainder $2x+1$, when divided by ${\left(x-1\right)}^2$. Find the remainder when $f\left(x\right)$ is divided by $\left(x-3\right){\left(x-1\right)}^2$.

What is Euclid's Division Algorithm?

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 :

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

State whether true or false:

$x-1$ a factor of $2x^4+3x^2-5x+7$?

If roots of the fourth degree polynomial: $2x^4+3x^3-11x^2-9x+15=0$ are $1,\pm \sqrt{3}$ and $p$, then the value of $p$

The roots of the cubic equation $x^3 – 23x^2 + 142x – 120$ are $1, 10 \mathrm{and} p$, then the value of $p$is

For a polynomial division, the divisor $g\left(x\right)=3x-2$, the quotient $q\left(x\right)=6x^2+4$, the remainder $r\left(x\right)=5$, the dividend $p\left(x\right)=18x^3-12x^2+12x+x$. Then the value of $x$ is 

Is $x-1$ a factor of $2x^4+3x^2-5x+7$?

Finding roots of the fourth degree polynomial: $2x^4+3x^3-11x^2-9x+15=0$.