Division of Algebraic Expressions

Divide: $(x^2+9x+18)÷(x+6)$.

Find the quotient $q\left(x\right)$ and remainder $r\left(x\right)$ on dividing $p\left(x\right)$ by $g\left(x\right)$. Verify the division algorithm. $p\left(x\right)=3x^3+2x^2+x+1; g\left(x\right)=x^3+3x+2$.

Divide $x^3-23x^2+142x-120$ by $x-1$ and then split the quotient.

Divide $44(x^4 -5x^3 -24x^2) \text{by} 11x(x-8)$

Divide $121x^3{y}^2{z}^2$ by $11x^2{y}^2{z}^2$.

Solve: $34x^3{y}^3{z}^3 ÷ 51x{y}^2{z}^3$

Can we write $x^3+x^2+x+1$ as $\frac{x^4-1}{x-1}= 0$ or $x^5+x^4+x^3+x^2+x+1$ as $\frac{x^6-1}{x-1}= 0$.

Prove that $n^7-7n^5+14n^3-8n$ is divisible by $840$ for all $\mathrm{n}$ in N.

Simplify :$\left(18t^2-98m^2\right)÷2(3t-7m)$

$\left(4a^2-64\right)÷(2a+8)=$

$\left(x^2-1\right)÷\left(x+2\right)$ is 

Divide $a^4-b^4$ by $a-b$.

Divide the given polynomial by the given monomial

$8(x^3{y}^2{z}^2+x^2{y}^3{z}^2+x^2{y}^2{z}^3)÷4x^2{y}^2{z}^2$

Divide the given polynomial by the given monomial

$\left(2a^{3}b-6a{b}^3\right)÷ab$

If $x^2-5x+6$ is divisible by $x-2$, then the quotient is

If $a^3+a=a\left(a^2+k\right)$ then find the value of $k.$

Verify if on dividing $15z^3-20z^2+13z-12$ by $3z-6$ we get quotient $=5z^2+\frac{10}{3}z+11$ and remainder $=54$.

Divide:

$\left(x^{2 }+9x+20\right)$ by $\left(x+4\right)$ ,

Find Adirai's percentage of marks who scored $25m^3{n}^{2}p$ out of $100m^{2}np$

Divide:

$10(4x-8y)$ by $5(x-2y)$