Question 36

x² + 5x + 2

The expression (x^3 + 4x² - 3x - 2) divided by (x - 1) simplifies to x² + 5x + 2, which is the correct answer. This result can be verified through polynomial long division.

A) x² + 4x - 3

This option is incorrect because it does not accurately represent the quotient obtained from the polynomial long division of (x^3 + 4x² - 3x - 2) by (x - 1). The coefficients and constant term do not match the correct answer.

B) x² + 4x + 2

This option is also incorrect. While it shares some components with the correct answer, the coefficient of the x term does not align with the results from the division, leading to an incorrect expression.

C) x² - 5x - 2

This option does not match the simplified expression at all, as both the coefficients of x and the constant term differ significantly from the result of the division, making it an invalid choice.

D) x² - 5x + 2

This option is incorrect as well. Similar to option C, the coefficients of x and the constant term do not reflect the outcome of the division, failing to satisfy the original polynomial division.

E) x² + 5x + 2

This is the correct option, as it accurately reflects the quotient obtained from dividing the polynomial (x^3 + 4x² - 3x - 2) by (x - 1). The coefficients and constant term perfectly match the result of the long division process.

Conclusion

The correct answer, x² + 5x + 2, is confirmed through polynomial long division, accurately representing the quotient of the given polynomial. All other options fail due to incorrect coefficients or constant terms, demonstrating that they do not correspond to the expected outcome of the division process.