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

To find the correct factors of the quadratic expression (2x^2 + xy - 3y^2), we can use the method of factoring by grouping or trial and error based on the coefficients of the terms.

The expression is a trinomial in the form of (ax^2 + bxy + cy^2). Here, (a = 2), (b = 1), and (c = -3).

To factor it, we look for two numbers that multiply to (ac = (2)(-3) = -6) and add to (b = 1). The pair of numbers that satisfy this are (3) and (-2). Therefore, we can rewrite the middle term:

[

2x^2 + 3xy - 2xy - 3y^2

]

Next, we group the terms:

[

(2x^2 + 3xy) + (-2xy - 3y^2)

]

Now, we factor out the common factors from each group:

[

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

]

This can be factored