Question

What is the remainder of the division (x³ −4x² +15x+7)+(x+2)

Answer 1

The remainder of the division is -69x² - 15x + 7.

Step-by-step explanation:

To find the remainder of the division of (x³ − 4x² + 15x + 7) divided by (x + 2), we can use long division.

1. Start by dividing x³ by x, which gives x².
2. Multiply (x + 2) by x², which gives x³ + 2x².
3. Subtract x³ + 2x² from x³ − 4x² + 15x + 7, which gives -6x² + 15x + 7.
4. Repeat the process with -6x² + 15x + 7.
5. Divide -6x² by x, which gives -6x.
6. Multiply (x + 2) by -6x, which gives -6x³ - 12x².
7. Subtract -6x³ - 12x² from -6x² + 15x + 7, which gives 27x² - 15x + 7.
8. Repeat the process with 27x² - 15x + 7.
9. Divide 27x² by x, which gives 27x.
10. Multiply (x + 2) by 27x, which gives 27x³ + 54x².
11. Subtract 27x³ + 54x² from 27x² - 15x + 7, which gives -69x² - 15x + 7.

The remainder of the division is -69x² - 15x + 7.