Question

Divide using long division. Check your answer. (x³ + 3x²-x+3)+(x-1) The quotient is with a remainder of (Simplify your answers. Do not factor.)

Answer 1

Let's perform the long division for \( \frac{x^3 + 3x^2 - x + 3}{x - 1} \).

```
x² + 4x + 3
______________________
x - 1 | x³ + 3x² - x + 3
- (x³ - x²)
______________
4x² - x
- (4x² - 4x)
______________
3x + 3
- (3x - 3)
______________
6
```

The quotient is \( x^2 + 4x + 3 \) with a remainder of 6.

So, \( \frac{x^3 + 3x^2 - x + 3}{x - 1} = x^2 + 4x + 3 + \frac{6}{x-1} \).