Question 1108098
two x to the fourth minus x cubed minus fifteen x squared plus three x divided by quantity x plus three



{{{(2x^4-x^3-15x^2+3)/(x+3)}}}


A term for x is needed, missing in your dividend so you will use dividend of
{{{2x^4-x^3-15x^2+0x+3}}},
and the coefficients are  2, -1, -15, 0, 3;
and the "root" to check is  {{{-3}}}.


<pre>
setup the synthetic division

-3   |   2   -1   -15   0   3
     |
     |
     ------------------------------

</pre>



<pre>
The Process for the synthetic division


-3   |   2   -1   -15   0   3
     |
     |        6    15   0   0
     ------------------------------
        2    5     0    0   3
</pre>

That means, the result for the division is  {{{2x^3+5x^2+3/(x+3)}}}
and you can convert this to a single rational form if you want.