Answer:
Step-by-step explanation:
To find the quotient of (x^3 + 8) divided by (x + 2), you can perform polynomial long division. Here's how you can do it:
1. Divide x^3 by x to get x^2:
- Write x^2 above x^3.
2. Multiply x^2 by (x + 2) to get x^3 + 2x^2:
- Write x^3 + 2x^2 below x^3 + 8, and subtract to get 6x^2.
3. Bring down the next term, which is 0x (since there is no x term):
- Write 0x below 6x^2.
4. Divide 6x^2 by x to get 6x:
- Write 6x above 0x.
5. Multiply 6x by (x + 2) to get 6x^2 + 12x:
- Write 6x^2 + 12x below 6x^2, and subtract to get -4x.
6. Bring down the constant term 8:
- Write 8 below -4x.
7. Divide -4x by x to get -4:
- Write -4 above 8.
8. Multiply -4 by (x + 2) to get -4x - 8:
- Write -4x - 8 below -4x, and subtract to get 16.
Since the remainder is 16, the quotient of (x^3 + 8) divided by (x + 2) is x^2 + 6x - 4 with a remainder of 16.
