What are the correct factors of x² + xy − 6y²?

Correct answer: (x + 3y)(x − 2y)

The correct answer is A: (x + 3y)(x − 2y). Since the first term is x², begin with two binomials whose first terms are x and x. We need two numbers, multiplied as coefficients of y, whose product is −6 and whose sum is +1, the coefficient of xy. The numbers are +3 and −2. Therefore write (x + 3y)(x − 2y). Expanding confirms it: x·x = x², x(−2y) = −2xy, 3y·x = 3xy, and 3y(−2y) = −6y². Combining the middle terms gives −2xy + 3xy = xy, exactly the original expression. Option B gives −xy as the middle term. Option C gives 5xy and −6y², while option D gives −5xy and −6y². Memory cue: for a monic trinomial, the two inner coefficients must have the required sum and product.