If x+3 is a factor then it will divide evenly into . So we can find the other factor by dividing 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):
-3 | 1 2 -5 -6
---- -3 3 6
---------------
1 -1 -2 0
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
factors fairly easily into (x-2)(x+1). So