Question 73115
To quickly do these kind of problems, we can use synthetic division. Let 4x+7=0 and solve for x. x=-7/4

<pre>

           -7/4 | 20  43  22
                |    -35 <---------------place product of 20 and -7/4 here
                -----------------
                  20  <-----------bring down leading coefficient
                                             </pre>

<pre>

           -7/4 | 20  43   22
                |    -35  -14 <-------------place product of -7/4 and 8 
                -----------------
                  20  8 <--------------add 43 and -35 and place sum here
                                             </pre>
<pre>

           -7/4 | 20  43   22
                |    -35  -14  
                -----------------
                  20  8    8  <--------------add 22 and -14 and place sum here
                                             </pre>

Since the last number is 8, this is the remainder. We add the remainder to the quotient. Each number under the bar is a coefficient so the answer looks like
{{{20x+8+8/(4x+7)}}}
This technique allows us to quickly divide and get the same answer as polynomial long division. Hope this makes sense, ask about synthetic division if it doesn't make any sense.