Question

How do you factor `x^5+2x^4-x-2`?

Answer 1

`x^5+2x^4-x-2=(x-1)(x+1)(x^2+1)(x+2)`

Explanation:

Use the difference of squares identity:

`a^2-b^2 = (a-b)(a+b)`

after factoring by grouping:

`x^5+2x^4-x-2`

`=(x^5+2x^4)-(x+2)`

`=x^4(x+2)-1(x+2)`

`=(x^4-1)(x+2)`

`=((x^2)^2-1^2)(x+2)`

`=(x^2-1)(x^2+1)(x+2)`

`=(x^2-1^2)(x^2+1)(x+2)`

`=(x-1)(x+1)(x^2+1)(x+2)`