Before starting, there's a formula that will be crucial to solving all this.
The formula states the following:
[tex]\dfrac{a+b}{c}= \dfrac{a}{c }+ \dfrac{b}{c}[/tex]
Polynomial 1:
[tex]\dfrac{12x^3+9x}{3x}[/tex]
Use the formula shown in the beginning of this answer.
[tex]\dfrac{12x^3}{3x}+ \dfrac{9x}{3x}[/tex]
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.
[tex]\dfrac{(4x^2)(3x)}{3x}+ \dfrac{3(3x)}{3x}[/tex]
[tex]=4x^2+3[/tex]
Polynomial 2:
[tex]\dfrac{8x^4 y^3 - 4x^7 y^5}{2xy^2}[/tex]
Use the formula shown in the beginning of the answer
[tex]\dfrac{8x^4 y^3}{2xy^2} - \dfrac{4x^7 y^5}{2xy^2}[/tex]
[tex]= \dfrac{(4x^3 y)(2xy^2)}{2xy^2} - \dfrac{(2x^6 y^3)(2xy^2)}{2xy^2}[/tex]
[tex]=4x^3y-2x^6y^3[/tex]
Polynomial 3:
[tex]\dfrac{4x^3+5x^2+3x}{x}[/tex]
Use the formula shown in the beginning of the problem (pretty much the same for 3 terms as well).
[tex]\dfrac{4x^3}{x}+\dfrac{5x^2}{x}+\dfrac{3x}{x}[/tex]
[tex]=4x^2+5x+3[/tex]
If you have any comments/questions, feel free to comment and I'll be happy to clarify.
