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

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

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

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 divisor of $f\left(x\right)$ is $x+a$ then find remainder.

$f\left(x\right)=2x-a$

If divisor of $f\left(x\right)$ is $x+a$ then find remainder.

$f\left(x\right)=x^2-a^2$

If divisor of $f\left(x\right)$ is $x+a$ then find remainder.

$f\left(x\right)=x^2-2x+1$

When a polynomial $f\left(x\right)$ is divided by $x^2-4$ then we get remainder $5x+6$. If the same polynomial divided by $x+2$ then what will be the remainder?

Divide $15$ by $3$ and check whether there is any relation between dividend and divisor.