Which of the following is a factor of u²+uv-2v²?

Rationale

(u-2v)

The expression u² + uv - 2v² can be factored as (u - 2v)(u + v). This shows that (u - 2v) is indeed a factor of the quadratic expression, making it the correct choice.

A ((u-v)) YOUR ANSWER

The expression (u - v) does not satisfy the factorization of u² + uv - 2v². When applying polynomial long division or substitution, it does not yield a product that matches the original expression, thus failing to act as a valid factor.

B ((2u-v)) YOUR ANSWER

The factor (2u - v) does not divide the expression u² + uv - 2v² evenly. Substituting values or performing polynomial division will show that this choice does not result in a product that replicates the quadratic, confirming it is not a factor.

C ((u-2v)) CORRECT

As previously noted, the expression u² + uv - 2v² can be factored as (u - 2v)(u + v). This confirms that (u - 2v) is a legitimate factor of the given expression, establishing it as the correct choice.

D ((u+v)) YOUR ANSWER

While (u + v) is part of the complete factorization, it cannot stand alone as a factor of u² + uv - 2v². It requires (u - 2v) to complete the factorization, which means it does not fulfill the criteria for being a separate factor.

Conclusion

The expression u² + uv - 2v² can be factored into the product of (u - 2v) and (u + v), identifying (u - 2v) as the valid factor. The other choices either do not divide the expression correctly or fail to be recognized as factors in their own right. Understanding factorization is crucial for simplifying polynomials and solving quadratic equations effectively.