Factor the polynomial:

a^4+2a^3-a-2

(a-1) * (a^2 + a-1) (a+2)

Step-by-step explanation:

a^4+2a^3-a-2

Lets factor by grouping

a^4-a + 2a^3-2

Factor out an a from the first group and a 2 from the second group

a (a^3 - 1) + 2 (a^3-1)

Factor out (a^3-1)

(a^3-1) (a+2)

We need to recognize that a^3-1 is the difference of cubes

(x^3-y^3) = (x-y) (x^2+xy+y^2)

Let x=a and y=1

(a-1) * (a^2 + a-1) (a+2)