Multiply: (x² - 3)(x^5 + 2x^3)

Rationale

x² - 3 and x^5 + 2x^3 multiply to give x^7, -3x^5, -6x^3.

When multiplying the two polynomials, each term in the first polynomial is multiplied by each term in the second, resulting in the coefficients and powers of x being combined appropriately. The correct expansion yields the terms x^7, -3x^5, and -6x^3.

A (x^7,-3x^5,-6x^3) CORRECT

This option accurately represents the result of the multiplication. The first term, x² multiplied by x^5, results in x^7. The second term, -3 multiplied by x^5, gives -3x^5. Lastly, the product of -3 and 2x^3 results in -6x^3, confirming that this option is indeed correct.

B (x^10,2x^5,-6x^3) YOUR ANSWER

Here, x^10 is incorrect as it suggests multiplying x² by x^5 should yield x^10, which is not accurate. The correct product of these terms is x^7. The second term, 2x^5, does not correctly represent the multiplication of -3 by any term from the second polynomial.

C (5x^5,2x^6,-6x^3) YOUR ANSWER

This option contains incorrect coefficients and exponents. The term 5x^5 does not arise from any multiplication of the given polynomials. Furthermore, 2x^6 incorrectly suggests a combination of terms that does not exist in this multiplication.

D (x^7,2x^5,-6) YOUR ANSWER

While x^7 is correct, the term 2x^5 does not accurately reflect the multiplication of -3 and x^5. Additionally, the final term -6 does not correspond to any product from the original polynomials.

Conclusion

The multiplication of the polynomials (x² - 3)(x^5 + 2x^3) results in the terms x^7, -3x^5, and -6x^3, making option A the correct answer. Each incorrect choice either misrepresents the coefficients or fails to correctly multiply the terms, demonstrating a misunderstanding of polynomial multiplication.

Multiply: (x² - 3)(x^5 + 2x^3)

x² - 3 and x^5 + 2x^3 multiply to give x^7, -3x^5, -6x^3.

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