Question 400453
{{{x^3 + 2x^2- 5x-6}}}
If x+3 is a factor it will divide evenly into this polynomial. And the quotient will be the other factor. So we divide to find the other factor.<br>
Synthetic division is easier than long divison for divisors like x+3. You just have to remember that synthetic division is designed for dividing by x-a. So we have to look at x+3 as if it was x-(-3):
<pre>
-3 |  1   2   -5   -6
----     -3    3    6
     ----------------
      1  -1   -2    0
</pre>
As the zero remainder (in the lower right corner) tells us, x+3 did divide evenly. And the rest of that bottom row tells us what the other factor is. "1 -1 -2" tells us the other factor is: {{{x^2-x-2}}}. So
{{{x^3 + 2x^2- 5x-6 = (x+3)(x^2-x-2)}}}
The second factor is a trinomial that is simple to factor:
{{{x^3 + 2x^2- 5x-6 = (x+3)(x^2-x-2) = (x+3)(x+1)(x-2)}}}