Question 812929
Whether you use long or synthetic division, it is important to notice that there is no {{{x^3}}} term in the dividend!<br>
{{{(x^4 -x^2 + 3x - 10) / (x + 5)}}}
Since synthetic division is usually easier I choose to divide this way. Since synthetic division is designed to work with divisors in the form of (x - c) [where 'c' is some number], we must think of the x+5 as x-(-5):
<pre>
-5 |    1   0   -1     3   -10
----       -5   25  -120   585
       ------------------------
        1  -5   24  -117   575
</pre>
The number in the lower right, 575, is the remainder. The rest of the bottom line is the quotient. The quotient of "1 -5 24 -117" translates into: {{{x^3-5x^2+24x-117}}}. So, after putting the remainder over the divisor, we get:
{{{(x^4 -x^2 + 3x - 10) / (x + 5) = x^3-5x^2+24x-117 + 575/(x+5)}}}