(x^3+4x²-3x-2)/(x-1)

Rationale

x^2 + 5x + 2

To find the result of the polynomial division of (x^3 + 4x² - 3x - 2) by (x - 1), we can use synthetic or polynomial long division, which ultimately yields x² + 5x + 2 as the quotient.

A (x² + 4x - 3) YOUR ANSWER

This choice miscalculates the coefficients of the polynomial. The term for x in this choice is incorrect, as the correct calculation yields a coefficient of 5, not 4.

B (x² + 4x + 2) YOUR ANSWER

While this option has the correct quadratic term, it inaccurately represents the linear term as well. Specifically, the coefficient of x should be 5, leading to an incorrect polynomial result.

C (x² - 5x - 2) YOUR ANSWER

This option misrepresents the signs of both the linear and constant terms. The negative coefficient in this expression results from an incorrect division process, which does not reflect the original polynomial accurately.

D (x² - 5x + 2) YOUR ANSWER

Like option C, this choice incorrectly alters both the linear and constant terms. It fails to correctly account for the coefficients derived from the polynomial long division, leading to further inaccuracies.

E (x^2 + 5x + 2) CORRECT

This choice accurately reflects the result of the polynomial division. The coefficients for both the x and constant terms are derived correctly from the division process, confirming it as the appropriate answer.

Conclusion

The polynomial division of (x^3 + 4x² - 3x - 2) by (x - 1) results in x² + 5x + 2, confirming that this expression correctly represents the quotient. The other options miscalculate the coefficients, leading to incorrect polynomial forms, while only choice E accurately reflects the result of the division.

(x^3+4x²-3x-2)/(x-1)

x^2 + 5x + 2

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