The image shows the first few steps of the polynomial division (x^2−4)÷(x−1). Complete the polynomial division process, then give the quotient and the remainder expressed as a fraction.

Answer 1

To perform polynomial division for (x^2 - 4) ÷ (x - 1), we set up the long division as follows:

```
x + 1
_______________
x - 1 | x^2 - 4 + 0x
- (x^2 - x)
___________
-5x - 4
```

To find the next term of the quotient, we divide x^2 by (x - 1), which gives us x. We then multiply x by (x - 1) to get x^2 - x, which we subtract from the dividend (x^2 - 4). This leaves us with -5x - 4.

To find the next term of the quotient, we divide -5x by (x - 1), which gives us -5. We then multiply -5 by (x - 1) to get -5x + 5, which we subtract from the remaining polynomial (-5x - 4). This leaves us with -9.

We cannot divide -9 by (x - 1) anymore, so the polynomial division is complete.

The quotient is x + 1 and the remainder is -9.

Expressing the quotient and remainder as a fraction:

Quotient: x + 1 can be written as (x + 1)/1.

Remainder: -9 can be written as -9/1.

Therefore, the quotient and remainder expressed as fractions are:

Quotient: (x + 1)/1

Remainder: -9/1