(6x ^ 3 - 3x ^ 2 + 2x) - (8x ^ 3 - 3x + 4) =

Rationale

- 2x ^ 3 - 3x ^ 2 + 5x - 4

To solve the expression ( (6x^3 - 3x^2 + 2x) - (8x^3 - 3x + 4) ), we first distribute the negative sign across the second polynomial, then combine like terms. The resulting simplified expression confirms that the answer is indeed (-2x^3 - 3x^2 + 5x - 4).

A (- 2x ^ 3 - 3x ^ 2 + 5x - 4) CORRECT

This choice accurately represents the result of the given polynomial subtraction. By simplifying, we have (6x^3 - 8x^3 = -2x^3), (-3x^2) remains unchanged, (2x + 3x = 5x), and (-4) comes from the constant term. Thus, this is the correct expression.

B (- 2x ^ 3 - 3x ^ 2 - x + 4) YOUR ANSWER

This option incorrectly combines the (x) terms, suggesting (2x - 3x) gives (-x) instead of (5x). The constant term also incorrectly adds (4). Therefore, this expression does not match the calculations performed.

C (- 2x ^ 3 + 2x - 4) YOUR ANSWER

In this choice, the (x) term is incorrectly simplified to (2x) instead of (5x), and the constant term of (-4) is correct but lacks the necessary (x) term. Thus, it does not represent the correct simplification of the polynomial.

D (- 2x ^ 3 + 2x + 4) YOUR ANSWER

This option also miscalculates the (x) term as (2x) and inaccurately adds (+4) instead of ( -4). Both errors make this choice incorrect as it fails to align with the proper simplification.

E (- 2x ^ 6 - 6x ^ 3 - 2x) YOUR ANSWER

This expression introduces an incorrect term of (x^6) and miscalculates the cubic term and linear term entirely. It does not relate to the original expression and is therefore invalid.

Conclusion

The correct answer to the polynomial subtraction is (-2x^3 - 3x^2 + 5x - 4), which results from accurate combining of like terms after distributing the negative sign. All other choices either miscalculate terms or incorrectly combine them, emphasizing the importance of precise algebraic manipulation in polynomial operations.

(6x ^ 3 - 3x ^ 2 + 2x) - (8x ^ 3 - 3x + 4) =

- 2x ^ 3 - 3x ^ 2 + 5x - 4

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