Division Algorithm for Polynomials

A number or expression that is to be divided by another is called Dividend.

An expression that is to be divided by another is called

If $f\left(x\right)=5x^5-x^3+3$ and $g\left(x\right)=5x^2+x-7$ then what is the degree of the quotient when $f\left(x\right)$ is divided by $g\left(x\right)$..

If $f\left(x\right)=5x^4-x^3+3$ and $g\left(x\right)=5x^2+x-7$ then what is the degree of the quotient when $f\left(x\right)$ is divided by $g\left(x\right)$..

If $f\left(x\right)=3x^4-x^3+2x+3$ and $g\left(x\right)=3x^2+2x+3$ then what is the degree of the quotient when $f\left(x\right)$ is divided by $g\left(x\right)$..

If $f\left(x\right)=2x^4+x^3+2x+3$ and $g\left(x\right)=3x^2+2x+3$ then what is the degree of the quotient when $f\left(x\right)$ is divided by $g\left(x\right)$..

When a polynomial $p\left(x\right)=2x^4-3x^3-3x^2+6x-2$ is divided by $g\left(x\right)$, the quotient we obtain is $2x^2-3x+1$ and the remainder is $0$, then $g\left(x\right)$ is

When we divide a polynomial $2x^2+3x+1$ by $\left(x+2\right)$, we get the quotient as $2x-1$ and the remainder as $3$

On dividing a polynomial $x^2-x-6$ by $g\left(x\right)$, we get the quotient as $\left(x+2\right)$ and the remainder as $0$, then find $g\left(x\right)$

If the polynomial $p\left(x\right)=x^2-x+1$ is divided by $\left(x-2\right)$ then the remainder is

By using division algorithm method find quotient and remainder when polynomial $P\left(x\right)=x^4-3x^2+4x-3$ is divided by $g\left(x\right)=x^2+1-x$.

The result of polynomial division of $x^3-4x^2+5x-2$ by $x-2$ is

Divide: $x^4-3x^2+4x+5$ by $x^2+1-x$ and find the remainder.

If polynomial $x^4-6x^3+16x^2-25x+10$ is divided by another polynomial $x^2-2x+k$ and leaves remainder comes $\left(x+a\right)$, then find the value of $k$ and $a$.

If $-2$ is the zero of the polynomial $f\left(x\right)=x^3+13x^2+32x+20$, then find the sum of all other zeros.

If $2\pm \sqrt{3}$ is a zero of the polynomial $f\left(x\right)=x^4-6x^3-26x^2+138x-35$, then find the sum of all other zeros.

If $\sqrt{2}$ and $-\sqrt{2}$ are zeros of the polynomial $f\left(x\right)=2x^4-3x^3-3x^2+6x-2$, then find the sum of all other zeros.

Divide second polynomial by first and verify that first polynomial is a factor of second polynomial.
$g\left(x\right)=x^3-3x+1$, $f\left(x\right)=x^5-4x^3+x^2+3x+1$

Divide second polynomial by first and verify that first polynomial is a factor of second polynomial.

$g\left(t\right)=t^2-3, f\left(t\right)=2t^4+3t^3-2t^2-9t-12$

Divide second polynomial by first and verify that first polynomial is a factor of second polynomial.
$g\left(x\right)=x^2+3x+1, f\left(x\right)=3x^4+5x^3-7x^2+2x+2$