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