Not all polynomials have a common factor in each term. In this case, they may sometimes by factored by grouping. Factoring by grouping can be attempted on any polynomial with four or more terms. However, not every such polynomial can be factored in this way.
Since the terms of the polynomial do not have a common factor (other than 1), the only option is to attempt to factor this polynomial by grouping.
The first two terms, x2 and 6x2, have a common factor of x2. The only common factor of the last two terms, x and 6, is 1. We are going to:
1. Factor out x2 from x3+6x2
2. Factor out 1 from x+6
3. Factor out the common binomial factor, x+6.
x3+6x2+x+6 = x2(x+6)+1(x+6) = (x+6) (x2+1)