Question 190881
Please help i am so confused and i keep coming up with these horrible fractions. this is supposed to be synthetic division.
<pre><font size = 4 color = "indigo"><b>
{{{(6t^4+5t^3-10t+4)/(3t-2)}}}

To divide {{{6t^4+5t^3-10t+4}}} by {{{3t-2}}} using synthetic
division:

1. Insert a placeholder term {{{" "+0t^2}}}
   making it {{{6t^4+5t^3+0t^2-10t+4}}} 
   divided by {{{3t-2}}}


2. Factor out the coefficient of t in the divisor 
   {{{3t-2}}}, getting {{{3(t-2/3)}}}.

3. Use synthetic division to divide by {{{t-2/3}}}

4. Divide the bottom row of the completed synthetic 
   division through by 3.

So:

First we divide by {{{t-2/3}}}.  We change the sign
of {{{-2/3}}} to {{{" "+2/3}}}.

{{{matrix(4,7,
2/3, "|",  6, 5, 0, -10, 4,
" ", "|", " ",4, 6,   4,-4,
" ", " ", "__","__","__","__","__",
" ", " ",  6, 9, 6,  -6, 0
                           )}}}  

Then we divide the bottom row through by 3, and 
get:

{{{matrix(1,5,2,3,2,-2,0)}}}

Which is interpreted as

{{{2t^3+3t^2+2t-2}}} with 0 remainder.

Edwin</pre>