Question

`( {x}^(3) + {x}^(2) + x + 2) / ({x}^(2) - 1)`

Answer 1

`(x^3+x^2+x+2) divide by (x^2-1)`

We use long division to divide

There is no x term in x^2 -1 so we put 0x

x + 1

----------------------------

x^2+0x-1 x^3+ x^2 + x+ 2

x^3+0x^2-x

-----------------------------(subtract the bottom from top)

x^2 +2x + 2

x^2 +0x - 1

--------------------------------(subtract the bottom from top)

2x + 3

-----------------------------------------

Quotient : x+1

Remainder : 2x+3