Question

Using synthetic division, find (x4 − 2) ÷ (x + 1).

Answer 1

-1 | 1 0 0 0 -2
. | -1 1 -1 1
- - - - - - - - - - - - - - -
. | 1 -1 1 -1 -1

which translates to


`(x^4-2)/(x+1)=x^3-x^2+x-1-\frac1{x+1}`

Answer 2

Answer with explanation:

`(x^4-2)/(x+1)\\\\=(x^4-1-1)/(x+1)\\\\=(x^4-1^4)/(x+1)-(1)/(x+1)\\\\=((x^2-1^2)(x^2+1^2))/(x+1)-(1)/(x+1)\\\\=((x-1)(x+1)(x^2+1))/(x+1)-(1)/(x+1)\\\\=(x-1)(x^2+1)-(1)/(x+1)\\\\=x * (x^2+1)-1* (x^2+1)-(1)/(x+1)\\\\=x^3+x-x^2-1-(1)/(x+1)\\\\=x^3-x^2+x-1-(1)/(x+1)`

Or

Writing the coefficient of
`x^4,x^3,x^2, x`

and made the table to solve by synthetic Division method.

Option A