1)x⁴+ 3x³- х²-х+6:х+3

To divide the polynomial \(x^4 + 3x^3 - x^2 - x + 6\) by \(x + 3\), we can use polynomial long division.

1. Divide the leading term of the numerator \(x^4\) by the leading term of the denominator \(x\) to get \(x^3\).

2. Multiply \(x^3\) by \(x + 3\) to get \(x^4 + 3x^3\).

3. Subtract \(x^4 + 3x^3\) from the original polynomial:

   \[ (x^4 + 3x^3 - x^2 - x + 6) - (x^4 + 3x^3) = -x^2 - x + 6 \]

4. Now, take the next term in the result, \(-x^2\), and divide it by \(x\) to get \(-x\).

5. Multiply \(-x\) by \(x + 3\) to get \(-x^2 - 3x\).

6. Subtract this result from \(-x^2 - x + 6\):

   \[ (-x^2 - x + 6) - (-x^2 - 3x) = 2x + 6 \]

7. Now divide \(2x\) by \(x\) which gives \(2\).

8. Multiply \(2\) by \(x + 3\) to get \(2x + 6\).

9. Subtract this from \(2x + 6\):

   \[ (2x + 6) - (2x + 6) = 0 \]

So the division is complete, and we find that:

\[ \frac{x^4 + 3x^3 - x^2 - x + 6}{x + 3} = x^3 - x + 2 \]

Thus, the result of the division is:

\[ \boxed{x^3 - x + 2} \]