What is the sum of the two polynomials? 4x² + 3x + 5 + x² + 6x - 3?

Rationale

5x² + 9x + 2

To find the sum of the two polynomials, we combine like terms from each polynomial. The result after combining the terms leads us to the polynomial 5x² + 9x + 2.

A (4x² + 9x + 2) YOUR ANSWER

This option incorrectly adds the x² terms. The sum of 4x² and x² should yield 5x², not 4x², making this choice incorrect.

B (5x² + 9x + 2) CORRECT

This option correctly combines the like terms. Adding the x² terms gives 5x², adding the x terms gives 9x, and combining the constant terms results in 2. This is the correct answer.

C (5x² + 9x + 8) YOUR ANSWER

While this option correctly sums the x² and x terms, it inaccurately combines the constant terms. The correct constant term should be 2, not 8, making this choice incorrect.

D (4x² + 9x² + 2) YOUR ANSWER

This option misrepresents the polynomial by incorrectly combining the x² terms. It suggests an addition that does not align with the original polynomials. The correct sum should only have one x² term, which is 5x².

E (5x² + 9x² + 8) YOUR ANSWER

Similar to option D, this choice inaccurately combines the x² terms, suggesting a total of 14x² instead of the correct 5x². Furthermore, it incorrectly states the constant term as 8.

Conclusion

The correct sum of the polynomials 4x² + 3x + 5 and x² + 6x - 3 is achieved by carefully combining like terms, resulting in the polynomial 5x² + 9x + 2. Each incorrect choice either miscalculates the sum of the x² terms, fails to add constants correctly, or combines terms inappropriately, highlighting the importance of accurate polynomial addition.