Divide using long division. Check your answer.
(x^3+3x^2-x+3)/(x-1)
To divide using long division, we will follow these steps:
Step 1: Divide the first term of the dividend by the first term of the divisor. Place the result as the first term of the quotient.
Step 2: Multiply the divisor by the quotient term obtained in step 1.
Step 3: Subtract the product obtained in step 2 from the dividend.
Step 4: Bring down the next term from the dividend to the remainder obtained in step 3.
Step 5: Repeat steps 1-4 until there are no more terms to bring down.
Let's apply these steps to the given problem:
```
x^2 + 4x + 3
______________________
x - 1 | x^3 + 3x^2 - x + 3
- x^3 + x^2
_______________
2x^2 - x + 3
- 2x^2 + 2x
___________
x - 3
```
The quotient is x^2 + 4x + 3, and the remainder is x - 3.
Therefore, the answer is (x^2 + 4x + 3) with a remainder of (x - 3).