Question 716670
{{{(5x^2 - 12x - 8)/(x + 3)}}}
is just an expression and expressions cannot be "solved". But they can be simplified. In this case we can divide the numerator by the denominator.<br>
Synthetic division is designed for division by an expression of the form:
x - n
where "n" is some number. If we are to use synthetic division to divide by x+3 we must imagine (or actually rewrite) it as a subtraction: x - (-3):
<pre>
-3  |   5   -12   -8
-----       -15   81
       -------------
        5   -27   73
</pre>The remainder is in the lower right corner. It is 73. The rest of the bottom row is the quotient. The "5 -27" translates into 5x-27. So after dividing:
{{{(5x^2 - 12x - 8)/(x + 3)}}}
we get:
{{{5x-27+73/(x+3)}}}
(Note what happens with the remainder. We handle in just the same way as in the "good old days" before variables: We make a fraction with the remainder on top and the divisor on the bottom!)