# How do you divide #(3x^4+22x^3+ 15 x^2+26x+8)/(x-2) #?

##### 1 Answer

Long divide the coefficients to find:

#(3x^4+22x^3+15x^2+26x+8)/(x-2) = 3x^3+28x^2+71x+168#

with remainder

#### Explanation:

There are other ways, but I like to long divide the coefficients like this:

A more compact form of this is called synthetic division, but I find it easier to read the long division layout.

Reassembling polynomials from the coefficients, we find:

#(3x^4+22x^3+15x^2+26x+8)/(x-2) = 3x^3+28x^2+71x+168#

with remainder

Or you can write:

#3x^4+22x^3+15x^2+26x+8#

#= (x-2)(3x^3+28x^2+71x+168) + 344#

Note that if you are long dividing polynomials that have a 'missing' term, then you need to include a

As a check, let

#f(2) = 3*16+22*8+15*4+26*2+8#

#=48+176+60+52+8#

#=344#