Question 384334
{{{x^3+2x^2-5x-6}}}
If x+3 is a factor then it will divide evenly into {{{x^3+2x^2-5x-6}}}. So we can find the other factor by dividing {{{x^3+2x^2-5x-6}}} by x+3. We can use long division or synthetic division. I find synthetic division easier. But synthetic division works for divisors in the form x-c where c is some number. So to use synthetic division with x+3 we have to look at it as a subtraction: x - (-3):
<pre>
-3 |  1   2   -5   -6
----     -3    3    6
      ---------------
      1  -1   -2    0
</pre>
The zero in the lower right corner is the remainder and a zero remainder means it (x - (-3)) divided evenly (as we were told it would). The rest of the bottom line  tells us the quotient (which is the other factor). The 1 -1 -2 translates into {{{x^2-x-2}}}<br>
{{{x^2-x-2}}} factors fairly easily into (x-2)(x+1). So
{{{x^3+2x^2-5x-6 = (x+3)(x-2)(x+1)}}}