Factor 15x^2 + 13xy - 44y^2: Quadratic Trinomial Factoring

The given expression is 15x^2 + 13xy - 44y^2.

To factor this quadratic trinomial, we follow these steps:

1. Find the product of the leading coefficient and the constant term: 15 * -44 = -660
2. Find two factors of the product that add up to the coefficient of the middle term: The factors 44 and -15 satisfy this condition (44 * -15 = -660 and 44 + -15 = 29)
3. Rewrite the middle term using the two factors: 15x^2 + 44xy - 15xy - 44y^2
4. Factor by grouping: (15x^2 + 44xy) + (-15xy - 44y^2)
5. Factor out the greatest common factor from each group: x(15x + 44y) - y(15x + 44y)
6. Factor out the common binomial: (15x + 44y)(x - y)

Therefore, the factored form of the expression 15x^2 + 13xy - 44y^2 is (15x + 44y)(x - y).