Question 22

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

To find the sum of the two polynomials, we combine like terms from the expression 4x² + 3x + 5 and x² + 6x - 3. This results in 5x² + 9x + 2.

A) 4x² + 9x + 2

This option incorrectly combines the first polynomial's quadratic term with the second polynomial's linear terms but fails to account for the x² from the second polynomial. Therefore, it does not represent the correct sum.

B) 5x² + 9x + 2

This option is correct as it accurately combines the like terms from both polynomials. Adding 4x² and x² gives 5x², while adding 3x and 6x results in 9x. Finally, combining the constants 5 and -3 yields 2.

C) 5x² + 9x + 8

This option incorrectly adds the constant terms together. While it correctly combines the x² and x terms, the constant terms 5 and -3 should sum to 2, not 8, making this option incorrect.

D) 4x² + 9x² + 2

This option misrepresents the terms by adding the x² terms improperly. It suggests that there are two separate x² terms from the first polynomial, which is incorrect. Thus, it does not yield the correct sum.

E) 5x² + 9x² + 8

This option is incorrect as it also misrepresents the x² terms. It incorrectly implies that there are multiple x² terms to be summed, resulting in an inaccurate polynomial expression.

Conclusion

The correct answer, 5x² + 9x + 2, accurately reflects the sum of the two polynomials by properly combining like terms. All other options fail due to either incorrect combinations of the terms or miscalculations of the constants, confirming that B is the definitive correct choice.