What is the sum of the two polynomials?

Rationale

5x² + 9x + 2

To find the sum of the two polynomials, we combine the coefficients of like terms from each polynomial expression. The resulting polynomial from this operation is 5x² + 9x + 2.

A (4x² + 9x + 2) YOUR ANSWER

This choice misrepresents the coefficient of the x² term. It suggests that the sum involves a total of 4x² instead of the correct 5x², which is derived from adding the relevant coefficients.

B (5x² + 9x + 2) CORRECT

This is the correct option. It accurately reflects the sum of the two polynomials by correctly combining the coefficients for the x² term, the x term, and the constant term.

C (5x² + 9x + 8) YOUR ANSWER

This choice correctly sums the x² and x terms but incorrectly adds the constant terms, suggesting a total of 8 instead of the correct value of 2.

D (4x^4 + 9x² + 2) YOUR ANSWER

This option incorrectly introduces an x⁴ term, which does not exist in the original polynomials being summed. The presence of x⁴ indicates a misunderstanding of the polynomial degree involved.

E (5x^4 + 9x^2 + 8) YOUR ANSWER

This choice also incorrectly introduces an x⁴ term and similarly miscalculates the constant term. It does not align with the structure of the original polynomials.

Conclusion

The correct polynomial resulting from the sum of the two given polynomials is 5x² + 9x + 2, as it correctly combines all like terms. The incorrect choices either miscalculate the coefficients or introduce extraneous terms that deviate from the original expressions, highlighting the importance of careful polynomial addition.