Question

Answer 1

`14)x^5+x+1`

`=x^5-x^2+x^2+x+1`

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

`=(x^2+x+1)(x^3-x^2+1)`

`15)x^5-x^4-1`

`=x^5-x^4+x^3-x^3-1`

`=x^3(x^2-x+1)-(x+1)(x^2-x+1)`

`=(x^2-x+1)(x^3-x-1)`

Answer 2

14: \(x^5+x+1=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)

15: \(x^5-x^4-1=\left(x^2-x+1\right)\left(x^3-x-1\right)\)

Answer 3

\(x^5+x+1=x^5-x^2+x^2+x+1\\ =x^2\left(x^3-1\right)+\left(x^2+x+1\right)\\ =x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left[x^2\left(x-1\right)+1\right]\)