Question

Factor the polynomial: a^4+2a^3-a-2

Answer 1

Answer:

(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)