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:

`(a+b)/(c)= (a)/(c )+ (b)/(c)`

Polynomial 1:


`(12x^3+9x)/(3x)`

Use the formula shown in the beginning of this answer.


`(12x^3)/(3x)+ (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.


`((4x^2)(3x))/(3x)+ (3(3x))/(3x)`


`=4x^2+3`

Polynomial 2:


`(8x^4 y^3 - 4x^7 y^5)/(2xy^2)`

Use the formula shown in the beginning of the answer


`(8x^4 y^3)/(2xy^2) - (4x^7 y^5)/(2xy^2)`


`= ((4x^3 y)(2xy^2))/(2xy^2) - ((2x^6 y^3)(2xy^2))/(2xy^2)`


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

Polynomial 3:


`(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).


`(4x^3)/(x)+(5x^2)/(x)+(3x)/(x)`


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

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