Question

Divide the following polynomials: (12x3 + 9x)/3x (8x4y3 – 4x7y5)/(2xy2) (4x3 +5x2 +3x)/x

Answer 1

Before starting, there's a formula that will be crucial to solving all this.

The formula states the following:
$\dfrac{a+b}{c}= \dfrac{a}{c }+ \dfrac{b}{c}$

Polynomial 1:

$\dfrac{12x^3+9x}{3x}$

Use the formula shown in the beginning of this answer.

$\dfrac{12x^3}{3x}+ \dfrac{9x}{3x}$

Now, we only have to simplify each term.
Since you're tackling problems such as these, you should be familiar on exponential rules, so I hope you can follow along.

$\dfrac{(4x^2)(3x)}{3x}+ \dfrac{3(3x)}{3x}$

$=4x^2+3$

Polynomial 2:

$\dfrac{8x^4 y^3 - 4x^7 y^5}{2xy^2}$

Use the formula shown in the beginning of the answer

$\dfrac{8x^4 y^3}{2xy^2} - \dfrac{4x^7 y^5}{2xy^2}$

$= \dfrac{(4x^3 y)(2xy^2)}{2xy^2} - \dfrac{(2x^6 y^3)(2xy^2)}{2xy^2}$

$=4x^3y-2x^6y^3$

Polynomial 3:

$\dfrac{4x^3+5x^2+3x}{x}$

Use the formula shown in the beginning of the problem (pretty much the same for 3 terms as well).

$\dfrac{4x^3}{x}+\dfrac{5x^2}{x}+\dfrac{3x}{x}$

$=4x^2+5x+3$

If you have any comments/questions, feel free to comment and I'll be happy to clarify.