Division by Polynomial with Multiple Terms

A line segment $\mathrm{AB}$ whose length is $28x$ unit is to be divided into two equal parts. What will be the length of each part?

If the area of a rectangle is $45x^2+30x$ square meter and its breadth is $15x$ meter then what will be the length?

Verify whether on dividing polynomial $x^2-5x+3$ by $x-3$ the remainder is zero or not.

Prove that on dividing the polynomial $4x^3+3x^2+2x-9$ by $x-1$ the remainder is zero.

Divide polynomial $a$ by polynomial $a-b$.

If divisor $=4x-7$, quotient $=x+1$, remainder $=0$ the what is the dividend.

If divisor $=3x^2-2x+2$, quotient $=x+1$, remainder $=3$ the what is the dividend.

Find the quotient and remainder on dividing $x^2-2xy+y^2$ by $x-y$.

Find the quotient and remainder on dividing $x^5+5x+3x^2+5x^3+3$ by $4x+x^2+2$.

Find the quotient and remainder on dividing $2y^3+4y^2+3y+1$ by $y+1$.

Find the quotient and remainder on dividing $6x^2-5x+1$ by $2x-1$.

Find the quotient and remainder on dividing polynomial $x^2-x+1$ by $x+1$.

Write the polynomial $x^2+2xy+y^2$ in the form of factors and divide by $x+y$.