Question 14

The sum of the two polynomials is 5x² + 9x + 2.

To find the sum of the two given polynomials, we combine like terms from each polynomial. When adding (4x² + 3x + 5) and (x² + 6x - 3), we obtain 5x² + 9x + 2.

A) 4x² + 9x + 2

This option incorrectly suggests that the sum of the polynomials does not include the x² term from the second polynomial. The first polynomial contributes 4x², and the second contributes 1x², resulting in a total of 5x², making this choice incorrect.

B) 5x² + 9x + 2

This option is correct. Adding the x² terms gives 5x² (4x² + 1x²), adding the x terms gives 9x (3x + 6x), and combining the constant terms results in 2 (5 - 3). Thus, this is the accurate sum of the two polynomials.

C) 5x² + 9x + 8

While this option correctly presents the x² and x terms, it incorrectly sums the constant terms. Instead of 8, the correct sum of the constants is 2. Therefore, this choice is incorrect.

D) 4x^4 + 9x² + 2

This option is incorrect because it misrepresents the degree of the polynomial. The highest degree term should be x², not x⁴, and while the constant term is correct, the x² term is inaccurately stated.

E) 5x^4 + 9x^2 + 8

This option is incorrect as it also misrepresents the degree of the polynomial. The highest degree term should be x², not x⁴, and it contains the wrong constant sum as well.

Conclusion

The correct answer, 5x² + 9x + 2, accurately reflects the sum of the two polynomials through proper addition of like terms. All other options fail either in the degree of the polynomial or in the summation of the constant terms, confirming that B is the definitive choice.