Question 2

x^3 - 8x² + 21x - 30

When multiplying the polynomials (x - 5) and (x² - 3x + 6), the resulting expression simplifies to x^3 - 8x² + 21x - 30.

A) x^3 - 8x² + 21x - 30

This option is correct as it accurately represents the product of the two polynomials. The calculation involves distributing (x - 5) across each term in (x² - 3x + 6), resulting in the correct coefficients for each term.

B) x^3 - 8x² - 21x - 30

This option is incorrect because it has the wrong sign for the linear term. The correct multiplication gives a positive coefficient for the x term, which this option fails to capture.

C) x^3 - 8x² - 9x - 30

This option is also incorrect. While it has the correct x^3 and x² terms, it incorrectly states the coefficient of the x term as -9 instead of the correct value of +21.

D) x^3 + 8x² + 21x + 30

This option is incorrect due to the wrong signs in the x² and constant terms. The signs must reflect the operations involved in the polynomial multiplication, which this choice does not.

E) x^3 + 8x^2 - 9x + 30

This option is incorrect as it contains multiple inaccuracies. It has the wrong sign for both the x² and constant terms, as well as an incorrect coefficient for the x term.

Conclusion

Option A is definitively the correct answer as it reflects the accurate product of the given polynomials. All other options contain errors in either the signs or the coefficients, failing to represent the result of the polynomial multiplication correctly. Thus, A stands as the only valid choice.