# How do you divide (3x^4+2x^2+5x)/(6x^2+12x+4)  using polynomial long division?

Oct 14, 2017

$\frac{1}{2} {x}^{2} - x + 2 - \frac{15 x + 8}{6 {x}^{2} + 12 x + 4}$

#### Explanation:

As it works well on Socratic use a format which really is the same thing as :

$6 {x}^{2} + 12 x + 4 \text{ } \overline{| 3 {x}^{4} + 2 {x}^{2} + 5 x}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
For formatting alignment I include place keepers. For example: $0 {x}^{3}$

$\textcolor{w h i t e}{\text{dddddddddddddddddddd}} 3 {x}^{4} + 0 {x}^{3} + 2 {x}^{2} + 5 x + 0$
color(magenta)(1/2x^2)(6x^2+12x+4) ->ul(color(white)("d")3x^4+6x^3+2x^2 larr" Subtract")
$\textcolor{w h i t e}{\text{dddddddddddddddddddddd")0 -6x^3+color(white)("d}} 0 {x}^{2} + 5 x + 0$
color(magenta)(-x)(6x^2+12x+4)->color(white)("ddd.dd")ul( -6x^3-12x^2-4x larr" Sub."
$\textcolor{w h i t e}{\text{dddddddddddddddddddddddddd")0color(white)("d}} + 12 {x}^{2} + 9 x + 0$
color(magenta)(2)(6x^2+12x+4)->color(white)("dddd")"Subtract"->ul( 12x^2+24x+8)
$\textcolor{w h i t e}{\text{ddddddddddddddddddd")color(magenta)("Remainder} \to - 0 - 15 x - 8}$

color(magenta)("1/2x^2-x+2 -(15x+8)/(6x^2+12x+4))