ASVAB Practice Test

What are the factors of 2x^2 + xy - 3y^2?

1. (2x - 3y)(x + y)

2. (2x + 3y)(x - y)

3. (2x + y)(x - 3y)

4. (x + y)(2x - 3y)

The correct answer is: (2x - 3y)(x + y)

The factors of the given expression can be found by looking for two binomials that can be multiplied together to give the original expression. In this case, option A is the only correct answer because it follows the pattern of (a + b)(c + d), where ac = 2x^2, ad = xy, bc = -3y^2. Option B is incorrect because if multiplied out, it yields 2x^2 + 3xy - 3xy - 3y^2, resulting in a middle term that does not match the original expression. Option C also results in a middle term that does not match the original expression. Option D only works if one of the terms in each binomial is a constant, which is not the case here. Therefore, option A is the only correct choice.