factor:
1)x^2+x-6
2)x^2+5x+6
3)x^2+6x+8
1. x²+x-6
When the coefficient of x²=1, only the factors of -6 need to be tried.
Make a table in which the first two columns represent all possible combination of integers whose product is -6, and the third column is their sum. We look for a sum of +1 (the coefficient of +x).
Factors sum
1 -6 -5
2 -3 -1 (reverse signs, since we look for +1)
3 -2 1
Therefore the factors are
(x+3)(x-2)
I will leave #2 and #3 as exercises.