Division of Algebraic Expressions

Complete the following table.

On dividing $x^4+2x^3+2x^2$ by $4x^2$ we get $\frac{1}{4}{x}^q+\frac{1}{2}x+\frac{1}{2}$ then find the value of $q$:

On dividing $27a^4-36a^2$ by $-9a$ we get $-T{a}^3+4a$ then find the value of $T.$

On dividing $5a^4{b}^3-10a^3{b}^2-15a^2{b}^2$ by $5a^2{b}^2$ we get $a^{2}b-2a-C$, then find the value of $C$.

On dividing  $2x^4-6x^3+4x^2$ by $2x^2$ we get $x^2-Mx+2$, then find the value of $M.$

If $\left(28a^4{b}^6{c}^8\right)÷\left(-7a^2{b}^4{c}^6\right)=-K{a}^2{b}^2{c}^2$ then find the value of $K$

Find the value of $k$, if $\left(32a^4{b}^{2}c\right)÷\left(-8abc\right)=k{a}^{3}b$

Find the value of $a+b$, if $\left(-x^5{y}^7\right)÷\left(-x^4{y}^5\right)=x^a{y}^b$

Find the value of $\left(-15x^3{y}^{2}z\right)÷\left(-5x^{2}yz\right)$

Find the value of $\left(18x^2{y}^2\right)÷\left(6xy\right)$

Divide and verify:

Dividend $=$ Divisor $\times$ quotient $+$ remainder.

$2x^3+3x^2+7x+15$ by $x^2+4$

Divide and verify:

Dividend $=$ Divisor $\times$ quotient $+$ remainder.

$9x^3-15x^2-5x+3$ by $3x+1$

Divide and verify:

Dividend $=$ Divisor $\times$ quotient $+$ remainder.

$a^3-2a^2+a+2$ by $a+2$

Divide and verify:

Dividend $=$ Divisor $\times$ quotient $+$ remainder.

$m^2-3m+7$ by $m-2$

Divide and prove that the divisor and the dividend are not multiple factors. Write down the quotient and the remainder for the following expression.

$8x^3-6x^2+10x+15$ by $\left(4x+1\right)$

Divide and prove that the divisor and the dividend are not multiple factors. Write down the quotient and the remainder for the following expression.

$4x^4-2x^3-10x^2+13x-6$ by $\left(2x+3\right)$

Divide and prove that the divisor and the dividend are not multiple factors. Write down the quotient and the remainder for the following expression.

$-12+3x^2-4x+x^3$ by $\left(x+5\right)$

Divide and prove that the divisor and the dividend are not multiple factors. Write down the quotient and the remainder for the following expression.

$x^3+2x^2+3x+4$ by $\left(x-1\right)$

Divide and say whether the divisor is multiple factors of the dividend.

$a^2+2ab+b^2$ by $\left(a+b\right)$

Divide and say whether the divisor is multiple factors of the dividend.

$x^3-5x^2-2x+24$ by $\left(x-4\right)$